Stability Analysis of Discrete-time Systems with Poisson-distributed Delays
|
|
- Leonard York
- 5 years ago
- Views:
Transcription
1 05 IEEE 54th Annual Conference on Decision Control (CDC) December 5-8, 05. Osaka, Japan Stability Analysis of Discrete-time Systems with Poisson-distributed Delays Kun Liu, Karl Henrik Johansson, Emilia Fridman Yuanqing Xia Abstract This paper is concerned with the stability analysis of linear discrete-time systems with poisson-distributed delays. Firstly, the exponential stability condition of system with poisson-distributed delays is derived when the corresponding system with the zero-delay or the system without the delayed term is asymptotically stable. Then, an augmented Lyapunov functional is suggested to hle the case that the corresponding system without the delay as well as the system without the delayed term are not necessary to be asymptotically stable. Furthermore, we show that the results can be further improved by formulating the system as a higher-order augmented one applying the corresponding augmented Lyapunov functional. Finally, the efficiency of the proposed results is illustrated by some numerical examples. Keywords: Infinite delays, poisson-distributed delays, stabilizing delays, Lyapunov method. I. INTRODUCTION Systems with distributed delays are frequently encountered in modeling the physiological behavior, the traffic flow, the population dynamics, the control over networks [9, [0. In general, there are two main classes of distributed delays, namely: finite distributed delays infinite distributed delays. A great number of results have been reported for the stability control of systems with finite distributed delays, e.g., [, [, [3, [ the reference therein. For the case of infinite distributed delays, we refer to [8, [9, [3, where necessary sufficient conditions for the stability of continuous-time systems with gamma-distributed delays were derived in the frequency domain. In the time domain, sufficient conditions for the stability of continuoustime systems with gamma-distributed delays were derived in [4 via appropriate Lyapunov functionals. Recently, the Lyapunov-based stability passivity analysis for diffusion partial differential equations with infinite distributed delays were presented in [5. Discrete-time systems with infinite distributed delays have been analyzed in the literature. For example, the synchronization problem for an array of coupled complex discrete-time networks with infinite distributed delays was investigated in [7. The state feedback control was considered in [6 for discrete-time stochastic systems with infinite distributed delays nonlinear disturbances. In [7 [8, the K. Liu is with the School of Automation, Beijing Institute of Technology, Beijing 0008, China. kunliu@kth.se. His work was done when he was with KTH Royal Institute of Technology. K. H. Johansson is with the ACCESS Linnaeus Centre School of Electrical Engineering, KTH Royal Institute of Technology, SE-00 44, Stockholm, Sweden. kallej@kth.se. E. Fridman is with the School of Electrical Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel. emilia@eng.tau.ac.il. Y. Xia is with the School of Automation, Beijing Institute of Technology, Beijing 0008, China. xia yuanqing@bit.edu.cn. robust H control problem was discussed for discrete-time fuzzy systems with infinite distributed delays. It should be pointed out that all the results reported in [7, [6, [7, [8 are concerned with constant kernel function. Moreover, when the corresponding system without the delay as well as the system without the delayed term are not asymptotically stable, the proposed methods in [7, [6, [7, [8 are not applicable. It is well-known that poisson distribution is widespread in queuing theory [4. In [, the experimental data on the arrivals of pulses in indoor environments revealed that each cluster s time-delay is poisson-distributed, see also [5 for more explanations. In the present paper, we consider linear discrete-time systems with poisson-distributed delays. The objective is to derive sufficient exponential stability conditions for the system via appropriate Lyapunov functionals. It is allowed that the corresponding system without the delay as well as the system without the delayed term are not asymptotically stable. Thus, the considered infinite distributed delays with a gap in the paper have stabilizing effects. We derive the results by transforming the system to an augmented one applying augmented Lyapunov functionals [, [4. Due to the effect of poisson-distributed delays, the augmented system contains not only distributed but also discrete delays. This is different from the continuous-time counterpart in [4 for the general case of gamma-distributed delays, where only distributed delays were included in the resulting augmented system. Furthermore, we show that the results can be further improved by formulating the system as a higher-order augmented one applying the corresponding augmented Lyapunov functional. The structure of the paper is organized as follows. Section II presents the systems with poisson-distributed delays the summation inequalities that will be employed. The exponential stability of systems with poisson-distributed delays is studied in Section III when the corresponding system without the delay or the system without the delayed term is asymptotically stable. Section IV shows the exponential stability conditions of systems with poisson-distributed delays when the corresponding system with the zero-delay as well as the system without the delayed term are allowed to be not asymptotically stable. Section V illustrates the efficiency of the presented approach with some examples. Finally, the conclusions the further work are stated in Section VI. Notations: The notations used throughout the paper are stard. The superscript T sts for matrix transposition, R n denotes the n dimensional Euclidean space with vector norm, R n m is the set of all n m real matrices. P 0 (P 0) means that P is positive definite (positive semi /5/$ IEEE 7736
2 definite). denotes the term that is induced by symmetry I represents the unit matrix of appropriate dimensions. The symbol Z + denotes the set of non-negative integers. II. SYSTEM DESCRIPTION Consider the following linear discrete-time system with poisson-distributed delays: x(k +) = Ax(k)+A + τ=0 p(τ)x(k τ), k Z+, () where x(k) R n is the state vector, the system matrices A A are constant with appropriate dimensions. The initial condition is given as col{x(0),x( ),x( ),...} = col{φ(0),φ( ),φ( ),...}. The functionp(θ) is a poisson distribution with a gap h Z + : p(θ) = { e θ h (θ h)! θ h, 0 θ < h. The gap h can be interpreted e.g., in the network as the minimal propagation delay, which is always strictly positive. The mean value of p is +h. Due to the fact that τ=0 p(τ)x(k τ) = τ=h = θ=0 p(τ)x(k τ) p(θ +h)x(k θ h), we arrive at the equivalent system to () as follows: x(k +)=Ax(k)+A + τ=0 P(τ)x(k τ h), k Z+, () where P(τ) = e τ τ!. Moreover, some elementary calculus shows that for scalar 0 < δ δ i h P(i) = δ h e (δ ) = p 0δ, δ i h (i+h)p(i) = δ h e (δ ) (δ +h) = p δ, p = pδ δ= = +h. The derivation of stability conditions for system () is based on the summation inequalities with infinite sequences formulated in the following lemma. Lemma Given an n n matrix R 0, an integer h 0, scalar functions M(i) R, α(i) R + \{0}, a vector function x(i) R n such that the series concerned are convergent. Then the inequality α(i) M(i) xt (i)rx(i) TR [ M0 M(i)x(i) +, M(i)x(i) (3) its double summation extension hold, where h j=k i h α(i) M(i) xt (j)rx(j) TR M j=k i h M(i)x(j) k j=k i h, M(i)x(j) M 0 = α (i) M(i), M h = α (i)(i+h) M(i). (4) (5) Proof: The proofs of (3) (4) follow from those in [4 by involving sums instead of integral. Since R 0, application of Schur complements implies that the following holds [ α(i) M(i) x T (i)rx(i) x T (i)m(i) α (i) M(i) R 0 (6) for any i [0,+, i Z +. Summation of (6) from 0 to + leads to [ α(i) M(i) xt (i)rx(i) xt (i)m(i) M 0 R 0. By Schur complements, the above matrix inequality yields (3). Furthermore, double summation of [ α(i) M(i) x T (j)rx(j) x T (j)m(i) α (i) M(i) R 0 from k i h to k in j from 0 to + in i, where j=k i h α (i) M(i) = M h Schur complements ensure that the inequality (4) holds. In the sequel, the summation inequalities (3) (4) with infinite sequences play an important role in the stability problem of discrete-time systems with poisson-distributed delays. III. STABILITY IN THE CASE THAT A OR A+A IS SCHUR STABLE Consider system (). It is assumed that A or A + A is Schur stable. Our stability analysis will be based on the following discrete-time Lyapunov functional: V(k) = x T (k)wx(k)+v G (k)+v H (k), V G (k) = s=k i h δk s P(i)x T (s)g x(s), V H (k)= i+h j= s=k j δk s P(i)η T (s)h η (s), (7) where 0 < δ <, W 0, G 0, H 0, η (k) = x(k +) x(k). (8) Remark The term V G (k) compensates the delayed term in () when A is Schur stable. The term V H (k) extends the triple integrals of [4 to discrete case. It compensates the summation term in x(k +) = (A+A )x(k) +A τ=0 P(τ)[x(k τ h) x(k), k Z+, allows us to derive stability conditions of system () when A + A is Schur stable whereas A is not. Moreover, the V H (k) term also improves the results provided that A is Schur stable. By the stard arguments for discrete-time systems, we arrive at the following linear matrix inequality (LMI) condition for exponential stability of (): 7737
3 Proposition Given scalars > 0, 0 < δ < an integer h 0, assume that there exist n n positive definite matrices W, G H, such that the following LMI holds: Ξ = Σ+F0 T WF 0 p δ FT H F +p F0H T F 0 0, (9) where Σ = diag{g δw, p 0δ G }, F 0 = [A A, F 0 = [A I A, F = [I I. Then the system () is exponentially stable with the decay rate δ. Proof: Denote f(k) = τ=0p(τ)x(k τ h), ξ(k) = col{x(k),f(k)}, k Z +. Taking difference of V(k) along () leads to V(k) = V(k +) δv(k) ξ T (k)f0 TWF 0ξ(k)+x T (k)(g δw)x(k) +p η T(k)H η(k) δi+h P(i)x T (k i h)g x(k i h) (0) s=k i h δi+h P(i)η T (s)h η (s). () Applying further the inequalities (3) (4), we obtain δi+h P(i)x T (k i h)g x(k i h) p 0δ ft (k)g f(k) p δ s=k i h δi+h P(i)η T (s)h η (s) TH s=k i h (s) P(i)η k s=k i h P(i)η (s) = p δ [x(k) f(k)t H [x(k) f(k) = p δ ξt (k)f TH F ξ(k). () (3) Then () (3) yield V(k) = V(k + ) δv(k) ξ T (k)ξξ(k) 0 if LMI (9) holds. Due to the fact that min (W) x(k) V(k) δ k V(0), V(0) β φ c, where β > 0 is a scalar φ c = sup s=0,,,... φ(s), the system () is exponentially stable with the decay rate δ for given scalars > 0 h 0. Remark IfAis Schur stable, Lyapunov functional (7) with H = 0 can be applied to yield the following simple but conservative LMI condition: [ G +A T WA δw A T WA p 0δ G +A T WA 0. IV. STABILITY IN THE CASE THAT A AND A+A ARE ALLOWED TO BE NOT SCHUR STABLE In this section, we will derive LMI conditions for the exponential stability of system (), where A A + A may not be Schur stable. This means that the considered infinite distributed delays with a gap have stabilizing effects. We provide two sufficient stability conditions, the efficiency of which is illustrated by the given examples below. A. Condition I: an augmented system From (0), it follows that system () can be transformed into the following augmented one: x(k +) = Ax(k)+A f(k), f(k +) = τ=0 e τ τ! x(k + τ h) = e x(k + h)+ τ= e τ τ! x(k + τ h) = e x(k + h)+ τ=0 e τ+ (τ+)! x(k τ h) = e Ax(k h)+e A f(k h) + τ=0 Q(τ)x(k τ h), (4) where Q(τ) = e τ+ (τ+)!. Remark 3 The stability of system (4) implies the stability of system (), but not vice versa. For a positive integer h, the effect of poisson-distributed delays leads to the augmented system (4) that contains one term τ=0 Q(τ)x(k τ h) corresponding to distributed delays, two terms e Ax(k h), e A f(k h) with discrete delays. This is different from the continuous-time counterpart in [4 for the general case of gamma-distributed delays, where only distributed delays were included in the resulting augmented system. Simple computation shows that δ i h Q(i) = δ h e (e /δ ) = q 0δ, δ i h (i+h)q(i) = δ h e [e /δ +δ(h )(e /δ ) = q δ, q 0 = q0δ δ= = e, q = qδ δ= = +(h )( e ). (5) Consider system (4) with both distributed discrete delays. We suggest the following discrete-time Lyapunov functional: [ ˆV(k)=ξ T (k)ŵξ(k)+ V Gi (k)+v Hi (k)+v Si (k), V G (k) = i= i+h j= s=k i h δk s Q(i)x T (s)g x(s), V H (k) = s=k j δk s Q(i)η T (s)h η (s), V S (k) = s=k h δk s x T (s)s x(s) +h j= h s=k+j δk s η T(s)R η (s), V S (k) = s=k h δk s f T (s)s f(s) +h j= h s=k+j δk s η T(s)R η (s), (6) where the terms V G (k) V H (k) are defined in (7), ξ(k) η (k) are given in (0) (8), respectively, 0 < δ <, G 0, H 0, S i 0, R i 0, i =,,, Ŵ = [ P Q Z 0, (7) η (k) = f(k +) f(k). (8) Here the last two terms V S (k) V S (k) are added to compensate, respectively, the delayed terms x(k h) f(k h) of (4). Therefore, for system (4) with h = 0, V S (k) V S (k) are not necessary. We derive conditions 7738
4 to guarantee exponential stability of system (4) in the following proposition: Proposition Given scalars > 0, 0 < δ < an integer h 0, let there exist n n positive definite matrices P,Z, G i, H i, S i, R i, i =,, an n n matrix Q such that (7) the following LMI are satisfied: ˆΞ = ˆΣ+ ˆF 0 TŴ ˆF 0 δ ˆF TŴ ˆF p ˆF δ TH ˆF +ˆF 0 T[p H +q H +h R ˆF 0 +h ˆFT 0 R ˆF0 q ˆF δ 5 TH ˆF 5 δ h ˆFT 3 R ˆF3 δ h ˆFT 4 R ˆF4 0, (9) where ˆΣ = diag{s + G + q 0 G, p 0δ G + S, δ h S, δ h S, q 0δ G }, [ A A ˆF 0 = 0 0 e A e, [ A I I ˆF =, ˆF0 = [A I A 0 I , ˆF 0 = [0 I e A e A I, ˆF = [I I 0 0 0, ˆF 3 = [I 0 I 0 0, ˆF5 = [q 0 I I, ˆF 4 = [0 I 0 I 0. Then the system (4) is exponentially stable with the decay rate δ. Proof: Define υ(k) = τ=0q(τ)x(k τ h) (0) ˆξ(k) = col{x(k),f(k),x(k h),f(k h),υ(k)}. By taking difference of ˆV(k) along (4) applying Jensen inequality with finite sequences (see e.g., [6), we have i= ξ T (k +)Ŵξ(k +) δξt (k)ŵξ(k) = ˆξ T (k)[ˆf 0 TŴ ˆF 0 δ ˆF TŴ ˆF ˆξ(k) [ V Gi (k +)+V Hi (k +)+V Si (k +) δv Gi (k) δv Hi (k) δv Si (k) ˆξ T (k)[ˆσ+ ˆFT 0 [p H +q H +h R ˆF 0 p δ ˆF T H ˆF +h ˆFT 0 R ˆF0 δ h ˆFT 3 R ˆF3 δ h ˆFT 4 R ˆF4 ˆξ(k) () +q 0δ υt (k)g υ(k) δi+h Q(i)x T (k i h)g x(k i h) s=k i h δi+h Q(i)η T(s)H η (s). () Applying further the inequality (3), we obtain δi+h Q(i)x T (k i h)g x(k i h) q 0δ υt (k)g υ(k). Furthermore, the application of (4) leads to q δ s=k i h δi+h Q(i)η T (s)h η (s) TH s=k i h (s) Q(i)η k s=k i h Q(i)η (s) = q δ [q 0x(k) υ(k) T H [q 0 x(k) υ(k) = q ˆξ δ T (k)ˆf 5 TH ˆF 5ˆξ(k). (3) (4) Therefore, () (4) yield ˆV(k) = ˆV(k +) δˆv(k) ˆξ T (k)ˆξˆξ(k). Then if LMI (9) holds for given scalars > 0 h 0, the system (4) is exponentially stable with the decay rate δ. B. Condition II: a higher-order augmented system For the case that A A + A are not necessary to be Schur stable, alternatively, we analyze the stability of system () by transforming () into the following higherorder augmented one: x(k +) = Ax(k)+A f(k), f(k +) = e Ax(k h)+e A f(k h)+υ(k), υ(k +) = e Ax(k h)+e A f(k h)+g(k), (5) where f(k) υ(k) are defined in (0) (0), respectively, Similar to (5), we have g(k) = τ=0u(τ)x(k τ h), U(τ) = e τ+ (τ+)!. δ i h U(i) = δ h e (e /δ δ ) = u 0δ, δ i h (i+h)u(i) =δ h e [δ +(h +δ )(e /δ δ ) = u δ, u 0 = u0δ δ= = e e, u = uδ δ= = e +(h )( e e ). For system (5), we introduce the following augmented Lyapunov functional: V(k)= x T (k) W x(k)+ [ i= V Gi (k)+v Hi (k)+v Si (k) +V G3 (k)+v H3 (k) with V G3 (k) = V H3 (k) = i+h j= s=k i h δk s U(i)x T (s)g 3 x(s), s=k j δk s U(i)η T (s)h 3 η (s), where the terms V Gi (k), V Hi (k) V Si (k), i =,, are defined in (6), 0 < δ <, G 3 0, H 3 0, x(k) = col{x(k), f(k), υ(k)}, η (k) is given by (8),, W = P Q Q Z Q 3 0. (6) R Remark 4 Differently from the continuous-time counterpart in [4 for the general case of gamma-distributed delays, to analyze stability of the higher-order augmented system (5) for poisson-distributed delays, two additional terms V G3 (k) V H3 (k) are necessary to compensate the term g(k) = τ=0 U(τ)x(k τ h) of (5). Following the proof of Proposition, we derive the following condition for exponential stability of system (5): Proposition 3 Given scalars > 0, 0 < δ < an integer h 0, let there exist n n positive definite matrices 7739
5 TABLE I COMPLEXITY OF DIFFERENT STABILITY CONDITIONS Method Decision variables Number order of LMIs Proposition.5n +.5n one of 3n 3n Proposition 6n +5n one of 7n 7n one of n n Proposition 3 9.5n +6.5n one of 8n 8n one of 3n 3n P, Z, R, S i, R i, i =,, G j, H j, j =,,3, n n matrices Q j, j =,,3, such that (6) the following LMI are feasible: Ξ = Σ+ F 0 T W F 0 δ F T W F p F δ H T F + F 0 T[p H +q H +u H 3 +h R F 0 +h FT 0 R F0 q F δ 5 TH F 5 u F δ 6 TH 3 F 6 δ h FT 3 R F3 δ h FT 4 R F4 0, (7) where Σ = diag{s + G + q 0 G + u 0 G 3, p 0δ G + S, δ h S, δ h S, q 0δ G, u 0δ G 3}, A A F 0 = 0 0 e A e A I 0, 0 0 e A e A 0 I F = I I , F0 = [A I A , I 0 F 0 = [0 I e A e A I 0, F = [I I , F 3 = [I 0 I 0 0 0, F5 = [q 0 I I 0, F 6 = [u 0 I I, F4 = [0 I 0 I 0 0. Then the system (5) is exponentially stable with the decay rate δ. Remark 5 Compare the number of scalar decision variables the resulting LMIs. See Table I for the complexity of different stability conditions. Note that Proposition 3 achieves less conservative results than Propositions on account of computational complexity (see examples below). Remark 6 The system () with poisson-distributed delays can be also transformed into an augmented system with respect to the state col{x(k),f(k),υ(k),g(k)}. By virtue of corresponding augmented Lyapunov functional, the achieved less conservative results suffer from more decision variables higher order LMIs. V. ILLUSTRATIVE EXAMPLES In this section, we provide two examples to demonstrate the efficiency of stability conditions. A. Example Consider the linear discrete-time system () with [ [ A = A = Here A + A is Schur stable whereas A is not. For the values of h given in Table II, by applying Propositions,. TABLE II EXAMPLE : MAXIMUM ALLOWABLE VALUES OF FOR DIFFERENT h [max \ h 0 8 Proposition Proposition Proposition with δ =, we obtain the maximum allowable values of that guarantee the asymptotic stability (see Table II). For δ = the stability region in the (, h) plane that preserves the asymptotic stability is depicted in Figs. 3 by using Propositions, 3, respectively. The simulation results in Figs. 3 verify that Proposition with the number {6n + 5n} n= = 34 of variables induces more dense stability region than Proposition with {.5n +.5n} n= = 9 variables, but guarantees sparser stability region than Proposition 3 with the number{9.5n + 6.5n} n= = 5 of variables. h Proposition Fig.. Example : stability region by Proposition with δ = h Proposition Fig.. Example : stability region by Proposition with δ = B. Example Consider the linear discrete-time system () with the coefficient matrices: [ [ A = A 0 =
6 9 8 Proposition 3 National Natural Science Foundation of China (grant no , ). h Fig. 3. Example : stability region by Proposition 3 with δ = It is worth mentioning that in this system both A A+A are not Schur stable. Thus, Proposition is not applicable. For h = 0 the allowable values of that guarantee the asymptotic stability of the system by Propositions 3 with δ =, are shown in Fig. 4. Therefore, the delays have stabilizing effects. It is observed that in comparison with Proposition, Proposition 3 improves the results but at the price of {3.5n +.5n} n= = 7 additional decision variables. Proposition Proposition Fig. 4. Example : allowable values of by Propositions 3 with h = 0 δ = VI. CONCLUSIONS In this paper, we have presented LMI conditions for exponential stability of linear discrete-time systems with poisson-distributed delays. Especially, by formulating the system as an augmented one we have hled the case of stabilizing delay, i.e., the corresponding system with the zero-delay as well as the system without the delayed term are not necessary to be asymptotically stable. Extensions of the proposed direct Lyapunov approach to networked control systems will be interesting topics for future research. REFERENCES [ W.H. Chen W.X. Zheng. Delay-dependent robust stabilization for uncertain neutral systems with distributed delays. Automatica, 43():95 04, 007. [ E. Fridman. New Lyapunov-Krasovskii functionals for stability of linear retarded neutral type systems. Systems & Control Letters, 43(4):309 39, 00. [3 E. Fridman G. Tsodik. H control of distributed discrete delay systems via discretized Lyapunov functional. European Journal of Control, 5():84 94, 009. [4 D. Gross, J. Shortle, J. Thompson, C. Harris. Fundamentals of queueing theory. John Wiley & Sons, 008. [5 S.A. Kotsopoulos K. Loannou. Hbook of Research on Heterogeneous Next Generation Networking: Innovations Platforms: Innovations Platforms. IGI Global, 008. [6 K. Liu E. Fridman. Delay-dependent methods the first delay interval. Systems & Control Letters, 64():57 63, 04. [7 Y.R. Liu, Z.D. Wang, J.L. Liang, X.H. Liu. Synchronization state estimation for discrete-time complex networks with distributed delays. IEEE Transactions on Systems, Man, Cybernetics, Part B: Cybernetics, 38(5):34 35, 008. [8 W. Michiels, C. I. Morarescu, S. I. Niculescu. Consensus problems with distributed delays, with application to traffic flow models. SIAM Journal on Control Optimization, 48():77 0, 009. [9 C.I. Morarescu, S.I. Niculescu, K. Gu. Stability crossing curves of shifted gamma-distributed delay systems. SIAM Journal on Applied Dynamical Systems, 6(): , 007. [0 J.P. Richard. Time-delay systems: An overview of some recent advances open problems. Automatica, 39(0): , 003. [ A. Saleh R. Valenzuela. A statistical model for indoor multipath propagation. IEEE Journal on Selected Areas in Communications, 5():8 37, 987. [ A. Seuret F. Gouaisbaut. Wirtinger-based integral inequality: application to time-delay systems. Automatica, 49(9): , 03. [3 R. Sipahi, F. M. Atay, S. I. Niculescu. Stability of traffic flow behavior with distributed delays modeling the memory effects of the drivers. SIAM Journal on Applied Mathematics, 68(3): , 007. [4 O. Solomon E. Fridman. New stability conditions for systems with distributed delays. Automatica, 49(): , 03. [5 O. Solomon E. Fridman. Stability passivity analysis of semilinear diffusion PDEs with time-delays. International Journal of Control, 88():80 9, 05. [6 Z.D. Wang, Y.R. Liu, G.L. Wei, X.H. Liu. A note on control of a class of discrete-time stochastic systems with distributed delays nonlinear disturbances. Automatica, 46(3): , 00. [7 G.L. Wei, G. Feng, Z.D Wang. Robust control for discrete-time fuzzy systems with infinite-distributed delays. IEEE Transactions on Fuzzy Systems, 7():4 3, 009. [8 Z.G. Wu, P. Shi, H.Y. Su, J. Chu. Reliable control for discretetime fuzzy systems with infinite-distributed delay. IEEE Transactions on Fuzzy Systems, 0(): 3, 0. VII. ACKNOWLEDGEMENT This work was partially supported by the Israel Science Foundation (grant no. 8/4), the Knut Alice Wallenberg Foundation, the Swedish Research Council, the 774
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution
More informationResults on stability of linear systems with time varying delay
IET Control Theory & Applications Brief Paper Results on stability of linear systems with time varying delay ISSN 75-8644 Received on 8th June 206 Revised st September 206 Accepted on 20th September 206
More informationDelay-dependent stability and stabilization of neutral time-delay systems
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust Nonlinear Control 2009; 19:1364 1375 Published online 6 October 2008 in Wiley InterScience (www.interscience.wiley.com)..1384 Delay-dependent
More informationDelay-Dependent Stability Criteria for Linear Systems with Multiple Time Delays
Delay-Dependent Stability Criteria for Linear Systems with Multiple Time Delays Yong He, Min Wu, Jin-Hua She Abstract This paper deals with the problem of the delay-dependent stability of linear systems
More informationNew Lyapunov Krasovskii functionals for stability of linear retarded and neutral type systems
Systems & Control Letters 43 (21 39 319 www.elsevier.com/locate/sysconle New Lyapunov Krasovskii functionals for stability of linear retarded and neutral type systems E. Fridman Department of Electrical
More informationStability of Linear Distributed Parameter Systems with Time-Delays
Stability of Linear Distributed Parameter Systems with Time-Delays Emilia FRIDMAN* *Electrical Engineering, Tel Aviv University, Israel joint with Yury Orlov (CICESE Research Center, Ensenada, Mexico)
More informationDelay-Dependent Exponential Stability of Linear Systems with Fast Time-Varying Delay
International Mathematical Forum, 4, 2009, no. 39, 1939-1947 Delay-Dependent Exponential Stability of Linear Systems with Fast Time-Varying Delay Le Van Hien Department of Mathematics Hanoi National University
More informationSTABILITY ANALYSIS FOR SYSTEMS WITH LARGE DELAY PERIOD: A SWITCHING METHOD. Received March 2011; revised July 2011
International Journal of Innovative Computing, Information and Control ICIC International c 2012 ISSN 1349-4198 Volume 8, Number 6, June 2012 pp. 4235 4247 STABILITY ANALYSIS FOR SYSTEMS WITH LARGE DELAY
More informationFilter Design for Linear Time Delay Systems
IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 49, NO. 11, NOVEMBER 2001 2839 ANewH Filter Design for Linear Time Delay Systems E. Fridman Uri Shaked, Fellow, IEEE Abstract A new delay-dependent filtering
More informationOn Dwell Time Minimization for Switched Delay Systems: Free-Weighting Matrices Method
On Dwell Time Minimization for Switched Delay Systems: Free-Weighting Matrices Method Ahmet Taha Koru Akın Delibaşı and Hitay Özbay Abstract In this paper we present a quasi-convex minimization method
More informationEXPONENTIAL STABILITY OF SWITCHED LINEAR SYSTEMS WITH TIME-VARYING DELAY
Electronic Journal of Differential Equations, Vol. 2007(2007), No. 159, pp. 1 10. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) EXPONENTIAL
More informationEects of small delays on stability of singularly perturbed systems
Automatica 38 (2002) 897 902 www.elsevier.com/locate/automatica Technical Communique Eects of small delays on stability of singularly perturbed systems Emilia Fridman Department of Electrical Engineering
More informationSTABILIZATION OF LINEAR SYSTEMS VIA DELAYED STATE FEEDBACK CONTROLLER. El-Kébir Boukas. N. K. M Sirdi. Received December 2007; accepted February 2008
ICIC Express Letters ICIC International c 28 ISSN 1881-83X Volume 2, Number 1, March 28 pp. 1 6 STABILIZATION OF LINEAR SYSTEMS VIA DELAYED STATE FEEDBACK CONTROLLER El-Kébir Boukas Department of Mechanical
More informationDelay-Dependent H 1 Control of Uncertain Discrete Delay Systems
European Journal of Control ():9 # EUCA Delay-Dependent H Control of Uncertain Discrete Delay Systems E. Fridman and U. Shaked Department of Electrical Engineering-Systems Tel-Aviv University Tel-Aviv
More informationDelay-dependent Stability Analysis for Markovian Jump Systems with Interval Time-varying-delays
International Journal of Automation and Computing 7(2), May 2010, 224-229 DOI: 10.1007/s11633-010-0224-2 Delay-dependent Stability Analysis for Markovian Jump Systems with Interval Time-varying-delays
More informationCorrespondence should be addressed to Chien-Yu Lu,
Hindawi Publishing Corporation Discrete Dynamics in Nature and Society Volume 2009, Article ID 43015, 14 pages doi:10.1155/2009/43015 Research Article Delay-Range-Dependent Global Robust Passivity Analysis
More informationA Delay-dependent Condition for the Exponential Stability of Switched Linear Systems with Time-varying Delay
A Delay-dependent Condition for the Exponential Stability of Switched Linear Systems with Time-varying Delay Kreangkri Ratchagit Department of Mathematics Faculty of Science Maejo University Chiang Mai
More informationSTABILIZATION FOR A CLASS OF UNCERTAIN MULTI-TIME DELAYS SYSTEM USING SLIDING MODE CONTROLLER. Received April 2010; revised August 2010
International Journal of Innovative Computing, Information and Control ICIC International c 2011 ISSN 1349-4198 Volume 7, Number 7(B), July 2011 pp. 4195 4205 STABILIZATION FOR A CLASS OF UNCERTAIN MULTI-TIME
More informationOn Design of Reduced-Order H Filters for Discrete-Time Systems from Incomplete Measurements
Proceedings of the 47th IEEE Conference on Decision and Control Cancun, Mexico, Dec. 9-11, 2008 On Design of Reduced-Order H Filters for Discrete-Time Systems from Incomplete Measurements Shaosheng Zhou
More informationResearch Article Delay-Dependent Exponential Stability for Discrete-Time BAM Neural Networks with Time-Varying Delays
Discrete Dynamics in Nature and Society Volume 2008, Article ID 421614, 14 pages doi:10.1155/2008/421614 Research Article Delay-Dependent Exponential Stability for Discrete-Time BAM Neural Networks with
More informationROBUST STABILITY TEST FOR UNCERTAIN DISCRETE-TIME SYSTEMS: A DESCRIPTOR SYSTEM APPROACH
Latin American Applied Research 41: 359-364(211) ROBUS SABILIY ES FOR UNCERAIN DISCREE-IME SYSEMS: A DESCRIPOR SYSEM APPROACH W. ZHANG,, H. SU, Y. LIANG, and Z. HAN Engineering raining Center, Shanghai
More informationA DELAY-DEPENDENT APPROACH TO DESIGN STATE ESTIMATOR FOR DISCRETE STOCHASTIC RECURRENT NEURAL NETWORK WITH INTERVAL TIME-VARYING DELAYS
ICIC Express Letters ICIC International c 2009 ISSN 1881-80X Volume, Number (A), September 2009 pp. 5 70 A DELAY-DEPENDENT APPROACH TO DESIGN STATE ESTIMATOR FOR DISCRETE STOCHASTIC RECURRENT NEURAL NETWORK
More informationFINITE HORIZON ROBUST MODEL PREDICTIVE CONTROL USING LINEAR MATRIX INEQUALITIES. Danlei Chu, Tongwen Chen, Horacio J. Marquez
FINITE HORIZON ROBUST MODEL PREDICTIVE CONTROL USING LINEAR MATRIX INEQUALITIES Danlei Chu Tongwen Chen Horacio J Marquez Department of Electrical and Computer Engineering University of Alberta Edmonton
More informationA new robust delay-dependent stability criterion for a class of uncertain systems with delay
A new robust delay-dependent stability criterion for a class of uncertain systems with delay Fei Hao Long Wang and Tianguang Chu Abstract A new robust delay-dependent stability criterion for a class of
More informationResearch Article Convex Polyhedron Method to Stability of Continuous Systems with Two Additive Time-Varying Delay Components
Applied Mathematics Volume 202, Article ID 689820, 3 pages doi:0.55/202/689820 Research Article Convex Polyhedron Method to Stability of Continuous Systems with Two Additive Time-Varying Delay Components
More informationNetworked Control With Stochastic Scheduling
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 60, NO., NOVEMBER 205 307 Networked Control With Stochastic Scheduling Kun Liu, Emilia Fridman, and Karl Henrik Johansson Abstract This note develops the time-delay
More informationConverse Lyapunov-Krasovskii Theorems for Systems Described by Neutral Functional Differential Equation in Hale s Form
Converse Lyapunov-Krasovskii Theorems for Systems Described by Neutral Functional Differential Equation in Hale s Form arxiv:1206.3504v1 [math.ds] 15 Jun 2012 P. Pepe I. Karafyllis Abstract In this paper
More informationOptimal algorithm and application for point to point iterative learning control via updating reference trajectory
33 9 2016 9 DOI: 10.7641/CTA.2016.50970 Control Theory & Applications Vol. 33 No. 9 Sep. 2016,, (, 214122) :,.,,.,,,.. : ; ; ; ; : TP273 : A Optimal algorithm and application for point to point iterative
More informationImproved delay-dependent globally asymptotic stability of delayed uncertain recurrent neural networks with Markovian jumping parameters
Improved delay-dependent globally asymptotic stability of delayed uncertain recurrent neural networks with Markovian jumping parameters Ji Yan( 籍艳 ) and Cui Bao-Tong( 崔宝同 ) School of Communication and
More informationResearch Article Delay-Range-Dependent Stability Criteria for Takagi-Sugeno Fuzzy Systems with Fast Time-Varying Delays
Journal of Applied Mathematics Volume 2012rticle ID 475728, 20 pages doi:10.1155/2012/475728 Research Article Delay-Range-Dependent Stability Criteria for Takagi-Sugeno Fuzzy Systems with Fast Time-Varying
More informationNew summation inequalities and their
New summation inequalities and their applications to discrete-time delay systems Le Van Hien and Hieu Trinh arxiv:505.06344v [math.oc] 3 May 05 Abstract This paper provides new summation inequalities in
More informationRobust Observer for Uncertain T S model of a Synchronous Machine
Recent Advances in Circuits Communications Signal Processing Robust Observer for Uncertain T S model of a Synchronous Machine OUAALINE Najat ELALAMI Noureddine Laboratory of Automation Computer Engineering
More informationLinear matrix inequality approach for synchronization control of fuzzy cellular neural networks with mixed time delays
Chin. Phys. B Vol. 21, No. 4 (212 4842 Linear matrix inequality approach for synchronization control of fuzzy cellular neural networks with mixed time delays P. Balasubramaniam a, M. Kalpana a, and R.
More informationRobust sampled-data stabilization of linear systems - An input delay approach
Robust sampled-data stabilization of linear systems - An input delay approach Emilia Fridman, Alexandre Seuret, Jean-Pierre Richard To cite this version: Emilia Fridman, Alexandre Seuret, Jean-Pierre Richard.
More informationROBUST QUANTIZED H CONTROL FOR NETWORK CONTROL SYSTEMS WITH MARKOVIAN JUMPS AND TIME DELAYS. Received December 2012; revised April 2013
International Journal of Innovative Computing, Information and Control ICIC International c 213 ISSN 1349-4198 Volume 9, Number 12, December 213 pp. 4889 492 ROBUST QUANTIZED H CONTROL FOR NETWORK CONTROL
More informationLyapunov Stability of Linear Predictor Feedback for Distributed Input Delays
IEEE TRANSACTIONS ON AUTOMATIC CONTROL VOL. 56 NO. 3 MARCH 2011 655 Lyapunov Stability of Linear Predictor Feedback for Distributed Input Delays Nikolaos Bekiaris-Liberis Miroslav Krstic In this case system
More informationOn Computing the Worst-case Performance of Lur'e Systems with Uncertain Time-invariant Delays
Article On Computing the Worst-case Performance of Lur'e Systems with Uncertain Time-invariant Delays Thapana Nampradit and David Banjerdpongchai* Department of Electrical Engineering, Faculty of Engineering,
More informationIN the multiagent systems literature, the consensus problem,
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II: EXPRESS BRIEFS, VOL. 63, NO. 7, JULY 206 663 Periodic Behaviors for Discrete-Time Second-Order Multiagent Systems With Input Saturation Constraints Tao Yang,
More informationStability Analysis of Linear Systems with Time-varying State and Measurement Delays
Proceeding of the th World Congress on Intelligent Control and Automation Shenyang, China, June 29 - July 4 24 Stability Analysis of Linear Systems with ime-varying State and Measurement Delays Liang Lu
More informationResearch Article Stabilization Analysis and Synthesis of Discrete-Time Descriptor Markov Jump Systems with Partially Unknown Transition Probabilities
Research Journal of Applied Sciences, Engineering and Technology 7(4): 728-734, 214 DOI:1.1926/rjaset.7.39 ISSN: 24-7459; e-issn: 24-7467 214 Maxwell Scientific Publication Corp. Submitted: February 25,
More informationH Synchronization of Chaotic Systems via Delayed Feedback Control
International Journal of Automation and Computing 7(2), May 21, 23-235 DOI: 1.17/s11633-1-23-4 H Synchronization of Chaotic Systems via Delayed Feedback Control Li Sheng 1, 2 Hui-Zhong Yang 1 1 Institute
More informationAutomatica. Exponential stability of linear distributed parameter systems with time-varying delays. Emilia Fridman a,, Yury Orlov b.
Automatica 45 (9) 194 1 Contents lists available at ScienceDirect Automatica journal homepage: www.elsevier.com/locate/automatica Brief paper Exponential stability of linear distributed parameter systems
More informationCONSTRAINED MODEL PREDICTIVE CONTROL ON CONVEX POLYHEDRON STOCHASTIC LINEAR PARAMETER VARYING SYSTEMS. Received October 2012; revised February 2013
International Journal of Innovative Computing, Information and Control ICIC International c 2013 ISSN 1349-4198 Volume 9, Number 10, October 2013 pp 4193 4204 CONSTRAINED MODEL PREDICTIVE CONTROL ON CONVEX
More informationObserver design for systems with non small and unknown time-varying delay
Observer design for systems with non small and unknown time-varying delay Alexandre Seuret, Thierry Floquet, Jean-Pierre Richard, Sarah Spurgeon To cite this version: Alexandre Seuret, Thierry Floquet,
More informationStability Analysis for Switched Systems with Sequence-based Average Dwell Time
1 Stability Analysis for Switched Systems with Sequence-based Average Dwell Time Dianhao Zheng, Hongbin Zhang, Senior Member, IEEE, J. Andrew Zhang, Senior Member, IEEE, Steven W. Su, Senior Member, IEEE
More informationRobust sampled-data stabilization of linear systems: an input delay approach
Automatica 40 (004) 44 446 www.elsevier.com/locate/automatica Technical Communique Robust sampled-data stabilization of linear systems: an input delay approach Emilia Fridman a;, Alexandre Seuret b, Jean-Pierre
More informationOn backwards and forwards reachable sets bounding for perturbed time-delay systems
*Manuscript Click here to download Manuscript: 0HieuNamPubuduLeAMC2015revision 2.pdf Click here to view linked References On backwards and forwards reachable sets bounding for perturbed time-delay systems
More informationInput/output delay approach to robust sampled-data H control
Systems & Control Letters 54 (5) 71 8 www.elsevier.com/locate/sysconle Input/output delay approach to robust sampled-data H control E. Fridman, U. Shaked, V. Suplin Department of Electrical Engineering-Systems,
More informationSmall Gain Theorems on Input-to-Output Stability
Small Gain Theorems on Input-to-Output Stability Zhong-Ping Jiang Yuan Wang. Dept. of Electrical & Computer Engineering Polytechnic University Brooklyn, NY 11201, U.S.A. zjiang@control.poly.edu Dept. of
More informationStatic Output Feedback Controller for Nonlinear Interconnected Systems: Fuzzy Logic Approach
International Conference on Control, Automation and Systems 7 Oct. 7-,7 in COEX, Seoul, Korea Static Output Feedback Controller for Nonlinear Interconnected Systems: Fuzzy Logic Approach Geun Bum Koo l,
More informationarxiv: v2 [math.oc] 14 Dec 2015
Cooperative Output Regulation of Discrete-Time Linear Time-Delay Multi-agent Systems Yamin Yan and Jie Huang arxiv:1510.05380v2 math.oc 14 Dec 2015 Abstract In this paper, we study the cooperative output
More informationAnalysis of stability for impulsive stochastic fuzzy Cohen-Grossberg neural networks with mixed delays
Analysis of stability for impulsive stochastic fuzzy Cohen-Grossberg neural networks with mixed delays Qianhong Zhang Guizhou University of Finance and Economics Guizhou Key Laboratory of Economics System
More informationNew Stability Criteria for Recurrent Neural Networks with a Time-varying Delay
International Journal of Automation and Computing 8(1), February 2011, 128-133 DOI: 10.1007/s11633-010-0564-y New Stability Criteria for Recurrent Neural Networks with a Time-varying Delay Hong-Bing Zeng
More informationResearch Article Delay-Dependent H Filtering for Singular Time-Delay Systems
Discrete Dynamics in Nature and Society Volume 211, Article ID 76878, 2 pages doi:1.1155/211/76878 Research Article Delay-Dependent H Filtering for Singular Time-Delay Systems Zhenbo Li 1, 2 and Shuqian
More informationCONTINUOUS GAIN SCHEDULED H-INFINITY OBSERVER FOR UNCERTAIN NONLINEAR SYSTEM WITH TIME-DELAY AND ACTUATOR SATURATION
International Journal of Innovative Computing, Information and Control ICIC International c 212 ISSN 1349-4198 Volume 8, Number 12, December 212 pp. 877 888 CONTINUOUS GAIN SCHEDULED H-INFINITY OBSERVER
More informationFUZZY CONTROL OF NONLINEAR SYSTEMS WITH INPUT SATURATION USING MULTIPLE MODEL STRUCTURE. Min Zhang and Shousong Hu
ICIC Express Letters ICIC International c 2008 ISSN 1881-803X Volume 2, Number 2, June 2008 pp. 131 136 FUZZY CONTROL OF NONLINEAR SYSTEMS WITH INPUT SATURATION USING MULTIPLE MODEL STRUCTURE Min Zhang
More informationComplexity Reduction for Parameter-Dependent Linear Systems
213 American Control Conference (ACC) Washington DC USA June 17-19 213 Complexity Reduction for Parameter-Dependent Linear Systems Farhad Farokhi Henrik Sandberg and Karl H. Johansson Abstract We present
More informationResearch Article H Consensus for Discrete-Time Multiagent Systems
Discrete Dynamics in Nature and Society Volume 05, Article ID 8084, 6 pages http://dx.doi.org/0.55/05/8084 Research Article H Consensus for Discrete- Multiagent Systems Xiaoping Wang and Jinliang Shao
More informationLINEAR QUADRATIC OPTIMAL CONTROL BASED ON DYNAMIC COMPENSATION. Received October 2010; revised March 2011
International Journal of Innovative Computing, Information and Control ICIC International c 22 ISSN 349-498 Volume 8, Number 5(B), May 22 pp. 3743 3754 LINEAR QUADRATIC OPTIMAL CONTROL BASED ON DYNAMIC
More informationDeakin Research Online
Deakin Research Online This is the published version: Phat, V. N. and Trinh, H. 1, Exponential stabilization of neural networks with various activation functions and mixed time-varying delays, IEEE transactions
More informationState estimation of uncertain multiple model with unknown inputs
State estimation of uncertain multiple model with unknown inputs Abdelkader Akhenak, Mohammed Chadli, Didier Maquin and José Ragot Centre de Recherche en Automatique de Nancy, CNRS UMR 79 Institut National
More informationPacket-loss Dependent Controller Design for Networked Control Systems via Switched System Approach
Proceedings of the 47th IEEE Conference on Decision and Control Cancun, Mexico, Dec. 9-11, 8 WeC6.3 Packet-loss Dependent Controller Design for Networked Control Systems via Switched System Approach Junyan
More informationStability Analysis and H Synthesis for Linear Systems With Time-Varying Delays
Stability Analysis and H Synthesis for Linear Systems With Time-Varying Delays Anke Xue Yong-Yan Cao and Daoying Pi Abstract This paper is devoted to stability analysis and synthesis of the linear systems
More informationResearch Article Input and Output Passivity of Complex Dynamical Networks with General Topology
Advances in Decision Sciences Volume 1, Article ID 89481, 19 pages doi:1.1155/1/89481 Research Article Input and Output Passivity of Complex Dynamical Networks with General Topology Jinliang Wang Chongqing
More informationDistributed Adaptive Synchronization of Complex Dynamical Network with Unknown Time-varying Weights
International Journal of Automation and Computing 3, June 05, 33-39 DOI: 0.007/s633-05-0889-7 Distributed Adaptive Synchronization of Complex Dynamical Network with Unknown Time-varying Weights Hui-Na
More informationIMPULSIVE CONTROL OF DISCRETE-TIME NETWORKED SYSTEMS WITH COMMUNICATION DELAYS. Shumei Mu, Tianguang Chu, and Long Wang
IMPULSIVE CONTROL OF DISCRETE-TIME NETWORKED SYSTEMS WITH COMMUNICATION DELAYS Shumei Mu Tianguang Chu and Long Wang Intelligent Control Laboratory Center for Systems and Control Department of Mechanics
More informationPositive observers for positive interval linear discrete-time delay systems. Title. Li, P; Lam, J; Shu, Z
Title Positive observers for positive interval linear discrete-time delay systems Author(s) Li, P; Lam, J; Shu, Z Citation The 48th IEEE Conference on Decision and Control held jointly with the 28th Chinese
More informationComplexity Reduction for Parameter-Dependent Linear Systems
Complexity Reduction for Parameter-Dependent Linear Systems Farhad Farokhi Henrik Sandberg and Karl H. Johansson Abstract We present a complexity reduction algorithm for a family of parameter-dependent
More informationController synthesis for positive systems under l 1-induced performance
Title Controller synthesis for positive systems under l 1-induced performance Author(s) Chen, X; Lam, J; Li, P; Shu, Z Citation The 24th Chinese Control and Decision Conference (CCDC 212), Taiyuan, China,
More informationTakagi Sugeno Fuzzy Sliding Mode Controller Design for a Class of Nonlinear System
Australian Journal of Basic and Applied Sciences, 7(7): 395-400, 2013 ISSN 1991-8178 Takagi Sugeno Fuzzy Sliding Mode Controller Design for a Class of Nonlinear System 1 Budiman Azzali Basir, 2 Mohammad
More informationStability and stabilization of 2D continuous state-delayed systems
20 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) Orlando, FL, USA, December 2-5, 20 Stability and stabilization of 2D continuous state-delayed systems Mariem Ghamgui,
More informationConvex Optimization Approach to Dynamic Output Feedback Control for Delay Differential Systems of Neutral Type 1,2
journal of optimization theory and applications: Vol. 127 No. 2 pp. 411 423 November 2005 ( 2005) DOI: 10.1007/s10957-005-6552-7 Convex Optimization Approach to Dynamic Output Feedback Control for Delay
More informationAn asymptotic ratio characterization of input-to-state stability
1 An asymptotic ratio characterization of input-to-state stability Daniel Liberzon and Hyungbo Shim Abstract For continuous-time nonlinear systems with inputs, we introduce the notion of an asymptotic
More informationControl under Quantization, Saturation and Delay: An LMI Approach
Proceedings of the 7th World Congress The International Federation of Automatic Control Control under Quantization, Saturation and Delay: An LMI Approach Emilia Fridman Michel Dambrine Department of Electrical
More informationNEW SUPERVISORY CONTROL USING CONTROL-RELEVANT SWITCHING
NEW SUPERVISORY CONTROL USING CONTROL-RELEVANT SWITCHING Tae-Woong Yoon, Jung-Su Kim Dept. of Electrical Engineering. Korea University, Anam-dong 5-ga Seongbuk-gu 36-73, Seoul, Korea, twy@korea.ac.kr,
More informationDelay-independent stability via a reset loop
Delay-independent stability via a reset loop S. Tarbouriech & L. Zaccarian (LAAS-CNRS) Joint work with F. Perez Rubio & A. Banos (Universidad de Murcia) L2S Paris, 20-22 November 2012 L2S Paris, 20-22
More informationResearch Article Robust Observer Design for Takagi-Sugeno Fuzzy Systems with Mixed Neutral and Discrete Delays and Unknown Inputs
Mathematical Problems in Engineering Volume 2012, Article ID 635709, 13 pages doi:101155/2012/635709 Research Article Robust Observer Design for Takagi-Sugeno Fuzzy Systems with Mixed Neutral and Discrete
More informationPI OBSERVER DESIGN FOR DISCRETE-TIME DECOUPLED MULTIPLE MODELS. Rodolfo Orjuela, Benoît Marx, José Ragot and Didier Maquin
PI OBSERVER DESIGN FOR DISCRETE-TIME DECOUPLED MULTIPLE MODELS Rodolfo Orjuela Benoît Marx José Ragot and Didier Maquin Centre de Recherche en Automatique de Nancy UMR 739 Nancy-Université CNRS 2 Avenue
More informationDelay-dependent L2-L-infinity model reduction for polytopic systems with time-varying delay
itle Delay-dependent L-L-infinity model reduction for polytopic systems with time-varying delay Authors) Wang, Q; Lam, J Citation he 8 IEEE International Conference on Automation and Logistics ICAL 8),
More informationOn Sontag s Formula for the Input-to-State Practical Stabilization of Retarded Control-Affine Systems
On Sontag s Formula for the Input-to-State Practical Stabilization of Retarded Control-Affine Systems arxiv:1206.4240v1 [math.oc] 19 Jun 2012 P. Pepe Abstract In this paper input-to-state practically stabilizing
More informationAn LMI Approach to Robust Controller Designs of Takagi-Sugeno fuzzy Systems with Parametric Uncertainties
An LMI Approach to Robust Controller Designs of akagi-sugeno fuzzy Systems with Parametric Uncertainties Li Qi and Jun-You Yang School of Electrical Engineering Shenyang University of echnolog Shenyang,
More informationEvent-triggered PI control: Saturating actuators and anti-windup compensation
Event-triggered PI control: Saturating actuators and anti-windup compensation Daniel Lehmann, Georg Aleander Kiener and Karl Henrik Johansson Abstract Event-triggered control aims at reducing the communication
More informationBisimilar Finite Abstractions of Interconnected Systems
Bisimilar Finite Abstractions of Interconnected Systems Yuichi Tazaki and Jun-ichi Imura Tokyo Institute of Technology, Ōokayama 2-12-1, Meguro, Tokyo, Japan {tazaki,imura}@cyb.mei.titech.ac.jp http://www.cyb.mei.titech.ac.jp
More informationFuzzy Observers for Takagi-Sugeno Models with Local Nonlinear Terms
Fuzzy Observers for Takagi-Sugeno Models with Local Nonlinear Terms DUŠAN KROKAVEC, ANNA FILASOVÁ Technical University of Košice Department of Cybernetics and Artificial Intelligence Letná 9, 042 00 Košice
More informationCHATTERING-FREE SMC WITH UNIDIRECTIONAL AUXILIARY SURFACES FOR NONLINEAR SYSTEM WITH STATE CONSTRAINTS. Jian Fu, Qing-Xian Wu and Ze-Hui Mao
International Journal of Innovative Computing, Information and Control ICIC International c 2013 ISSN 1349-4198 Volume 9, Number 12, December 2013 pp. 4793 4809 CHATTERING-FREE SMC WITH UNIDIRECTIONAL
More informationReducing the Computational Cost of the Sum-of-Squares Stability Test for Time-Delayed Systems
Reducing the Computational Cost of the Sum-of-Squares Stability Test for Time-Delayed Systems Yashun Zhang Matthew Peet and Keqin Gu Abstract This paper considers the problem of reducing the computational
More informationAdaptive synchronization of chaotic neural networks with time delays via delayed feedback control
2017 º 12 È 31 4 ½ Dec. 2017 Communication on Applied Mathematics and Computation Vol.31 No.4 DOI 10.3969/j.issn.1006-6330.2017.04.002 Adaptive synchronization of chaotic neural networks with time delays
More informationIN the past decades, neural networks have been studied
Proceedings of the International MultiConference of Engineers and Computer Scientists 18 Vol II IMECS 18 March 14-1 18 Hong Kong Mixed H-infinity and Passivity Analysis for Neural Networks with Mixed Time-Varying
More informationSwitching H 2/H Control of Singular Perturbation Systems
Australian Journal of Basic and Applied Sciences, 3(4): 443-45, 009 ISSN 1991-8178 Switching H /H Control of Singular Perturbation Systems Ahmad Fakharian, Fatemeh Jamshidi, Mohammad aghi Hamidi Beheshti
More informationDiscrete-Time Distributed Observers over Jointly Connected Switching Networks and an Application
1 Discrete-Time Distributed Observers over Jointly Connected Switching Networks and an Application Tao Liu and Jie Huang arxiv:1812.01407v1 [cs.sy] 4 Dec 2018 Abstract In this paper, we first establish
More informationStrong stability of neutral equations with dependent delays
Strong stability of neutral equations with dependent delays W Michiels, T Vyhlidal, P Zitek, H Nijmeijer D Henrion 1 Introduction We discuss stability properties of the linear neutral equation p 2 ẋt +
More informationRobust Control for Nonlinear Discrete-Time Systems with Quantitative Input to State Stability Requirement
Proceedings of the 7th World Congress The International Federation of Automatic Control Robust Control for Nonlinear Discrete-Time Systems Quantitative Input to State Stability Requirement Shoudong Huang
More informationResearch Article Finite-Time Robust Stabilization for Stochastic Neural Networks
Abstract and Applied Analysis Volume 212, Article ID 231349, 15 pages doi:1.1155/212/231349 Research Article Finite-Time Robust Stabilization for Stochastic Neural Networks Weixiong Jin, 1 Xiaoyang Liu,
More informationDesign of Observer-Based 2-d Control Systems with Delays Satisfying Asymptotic Stablitiy Condition
Proceedings of the 2nd WSEAS International Conference on Dynamical Systems Control, Bucharest, Romania, October 16-17, 26 18 Design of Observer-Based 2-d Control Systems with Delays Satisfying Asymptotic
More informationStability Theory for Nonnegative and Compartmental Dynamical Systems with Time Delay
1 Stability Theory for Nonnegative and Compartmental Dynamical Systems with Time Delay Wassim M. Haddad and VijaySekhar Chellaboina School of Aerospace Engineering, Georgia Institute of Technology, Atlanta,
More informationRobust Output Feedback Control for Fractional Order Nonlinear Systems with Time-varying Delays
IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 3, NO. 4, OCTOBER 06 477 Robust Output Feedback Control for Fractional Order Nonlinear Systems with Time-varying Delays Changchun Hua, Tong Zhang, Yafeng Li,
More informationMultiple-mode switched observer-based unknown input estimation for a class of switched systems
Multiple-mode switched observer-based unknown input estimation for a class of switched systems Yantao Chen 1, Junqi Yang 1 *, Donglei Xie 1, Wei Zhang 2 1. College of Electrical Engineering and Automation,
More informationStability of Delay Impulsive Systems with Application to Networked Control Systems
Stability of Delay Impulsive Systems with Application to Networked Control Systems Payam Naghshtabrizi, João P. Hespanha, and Andrew R. Teel Abstract We establish asymptotic and exponential stability theorems
More informationROBUST PASSIVE OBSERVER-BASED CONTROL FOR A CLASS OF SINGULAR SYSTEMS
INTERNATIONAL JOURNAL OF INFORMATON AND SYSTEMS SCIENCES Volume 5 Number 3-4 Pages 480 487 c 2009 Institute for Scientific Computing and Information ROBUST PASSIVE OBSERVER-BASED CONTROL FOR A CLASS OF
More informationAnalysis and design of switched normal systems
Nonlinear Analysis 65 (2006) 2248 2259 www.elsevier.com/locate/na Analysis and design of switched normal systems Guisheng Zhai a,, Xuping Xu b, Hai Lin c, Anthony N. Michel c a Department of Mechanical
More information