This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and
|
|
- Homer Booker
- 6 years ago
- Views:
Transcription
1 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 and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier s archiving and manuscript policies are encouraged to visit:
2 Automatica (9) 7 77 Contents lists available at ScienceDirect Automatica journal homepage: Technical communique New conditions for delay-derivative-dependent stability, Emilia Fridman, Uri Shaked, Kun Liu School of Electrical Engineering, Tel-Aviv University, Tel-Aviv 9978, Israel a r t i c l e i n f o a b s t r a c t Article history: Received 8 January 9 Received in revised form August 9 Accepted 9 August 9 Available online September 9 Keywords: Time-varying delay Lyapunov Krasovskii functional LMI Two recent Lyapunov-based methods have significantly improved the stability analysis of time-delay systems: the delay-fractioning approach of Gouaisbaut and Peaucelle () for systems with constant delays and the convex analysis of systems with time-varying delays of Park and Ko (7). In this paper we develop a convex optimization approach to stability analysis of linear systems with interval timevarying delay by using the delay partitioning-based Lyapunov Krasovskii Functionals (LKFs). Novel LKFs are introduced with matrices that depend on the time delays. These functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives. 9 Elsevier Ltd. All rights reserved.. Introduction Over the past decades, much effort has been invested in the analysis and design of systems with time delays (see e.g. Fridman & Shaked, ; Hale & Lunel, 99; He, Wang, Lin, & Wu, 7; Kolmanovskii & Myshkis, 999; Niculescu, ; Richard, ). Among the recent advances in this area, two Lyapunovbased methods should be mentioned that significantly improved the stability analysis: the convex analysis of systems with timevarying delays of Park and Ko (7) and the delay-fractioning approach of Gouaisbaut and Peaucelle () for systems with constant delays. These recent methods inspired the present work, where we extend the delay partitioning approach to systems with interval time-varying delay in a convex way. We introduce novel LKFs with matrices that depend on the time delays. This enables us to derive LMI conditions that depend not only on the upper, but also on the lower bound of the delay derivative. The efficiency of the new stability criteria is demonstrated via numerical examples.. Stability of systems with time-varying delay Consider the system ẋ(t) = Ax(t) + A x(t τ(t)), () The material in this paper was presented at ROCOND 9, June 9. This paper was recommended for publication in revised form by Associate Editor Keqin Gu under the direction of Editor André L. Tits. This work was partially supported by Kamea Fund of Israel, by C&M Maus Chair at Tel-Aviv University and by China Scholarship Council. Corresponding author. Tel.: ; fax: addresses: emilia@eng.tau.ac.il (E. Fridman), shaked@eng.tau.ac.il (U. Shaked), liukun@eng.tau.ac.il (K. Liu). -98/$ see front matter 9 Elsevier Ltd. All rights reserved. doi:./j.automatica.9.8. where τ(t) [h a, h b, h a and where A and A are constant matrices. The delay is assumed to be either differentiable with d τ(t) d, () where d and d are given bounds, or fast-varying (with no restrictions on the delay derivative). The initial condition is given by x(t + θ) = φ(θ), θ [ h b,, φ W, where W is the space of absolutely continuous functions φ : [ h b, R n with the square integrable derivative and with the norm φ W = φ() + h b [ φ(s) + φ(s) ds... A delay partitioning approach to stability We divide the delay interval [h a, h b into two segments: [h, h and [h, h, where we denote h = h a, h = h b and h = (h a + h b )/. Then, () can be represented as ẋ(t) = Ax(t) + χ [h,h (τ(t))a x(t τ(t)) + [ χ [h,h (τ(t))a x(t τ(t)), () where χ [h,h : R {, } is the characteristic function of [h, h {, if s [h, h χ [h,h (s) =, otherwise. Consider the following Lyapunov functional: V(t, x t, ẋ t ) = x T (t)p(τ(t))x(t) + + t h x T (s)s x(s)ds + h t h h x T (s)qx(s)ds t τ(t) ξ T S S (s) ξ(s)ds S
3 7 E. Fridman et al. / Automatica (9) (h i+ h i ) i= hi ẋ T (s)r i ẋ(s)dsdθ, () h i+ t+θ where h =, ξ(s) = col{x(s), x(s ( ))}, S S Q, R i >, S >, >. () S We seek P(τ(t)) P(t) of the form [ τ(t) h P(τ(t)) = χ [h,h (τ(t)) [ τ(t) h + [ χ [h,h (τ(t)) i.e. τ(t) h P(τ(t)) = τ(t) h P + h τ(t) P P + h τ(t) P, () P + h τ(t) P, h τ(t) h, P + h τ(t) P, h < τ(t) h, where P k >, k =,,. Note that the function P(t) is continuous in t, since lim τ(t) h P(τ(t)) = P. Following (Hale & Lunel, 99), we define V(t, x t, ẋ t ) = lim sup s + s [V(t + s, x t+s, ẋ t+s ) V(t, x t, ẋ t ). (7) We are seeking for conditions guaranteeing that V α x(t) (8) for some scalar α >. We first consider τ h. We have [ χ(p P P(t) ) ( χ)(p P ) τ h = τ(t) +. (9) Denoting V = x T (t)p(τ(t))x(t), we find [ V τ h = x T (t) P(t)x(t) + ẋ T (t) χ + h τ(t) P + ( χ) [ τ(t) h Moreover, d [ (h i+ h i ) dt i= hi h i+ [ τ(t) h P P + h τ(t) P x(t). () t+θ [ = ẋ T (t) (h i+ h i ) R i ẋ(t) i= (h i+ h i ) i= hi ẋ T (s)r i ẋ(s)dsdθ t h i+ ẋ T (s)r i ẋ(s)ds. () We start with the case of τ [h, h ), where χ =. Using t h j the fact that t h j+ f j (s)ds = τ(t) f t h j (s)ds j+ + h j t τ(t) f j(s)ds,where f j (s) = ẋ T (s)r j ẋ(s), we apply Jensen s inequality (Gu, Kharitonov, & Chen, ) hi [(h i+ h i )f i (s)ds t h i+ hi ẋ T (s)dsr i t h i+ hi ẋ(s)ds, t h i+ hj t τ(t) τ(t) [(h j+ h j )f j (s)ds (τ(t) h j )(h j+ h j )v T j R jv j, t h j+ [(h j+ h j )f j (s)ds (h j+ τ(t))(h j+ h j )v T j R jv j, where v j = τ(t) h j τ(t) hj t τ(t) ẋ(s)ds, v j = h j+ τ(t) t h j+ ẋ(s)ds, () and j =, i =,. Here, for τ(t) h j, we have hj lim ẋ(s)ds = ẋ(t h j ). τ(t) h j τ(t) h j t τ(t) t τ(t) For h j+ τ(t) the vector ẋ(s)ds is defined h j+ τ(t) t h j+ similarly as ẋ(t h j+ ). We thus find V τ<h [ V τ<h + ẋ T (t) (h i+ h i ) R i ẋ(t) i= + x T (t)s x(t) x T (t h )S x(t h ) T x(t h ) S S + x(t h ) x(t h ) S x(t h ) T x(t h ) S S x(t h ) x(t h ) S x(t h ) [x(t) x(t h ) T R [x(t) x(t h ) [x(t h ) x(t h ) T R [x(t h ) x(t h ) (τ(t) h j )(h j+ h j )v T j R jv j (h j+ τ(t))(h j+ h j )v T j R jv j + x T (t h )Qx(t h ) ( τ(t))x T (t τ(t))qx(t τ(t)). () where j =, i =,. We insert free-weighting n n-matrices T, W, Y k, Z k (k =, ) by adding the following expressions to V(t) τ<h : = [x T (t)y T + ẋt (t)y T + xt (t τ(t))t T [ x(t h ) + x(t τ(t)) + (τ(t) h )v, = [x T (t)z T + ẋt (t)z T + xt (t h )W T [x(t h ) + (h τ(t))v x(t τ(t)). () We further use the descriptor method, where the right-hand side of the expression = [x T (t)p T j + ẋt (t)p T j [Ax(t) + A x(t τ(t)) ẋ(t), () with some n n-matrices P j, P j is added into the right-hand side of (). Setting η j (t) = col{x(t), ẋ(t), x(t h ), x(t h ), v j, v j, x(t τ(t)), x(t h )}, we obtain that along () V τ<h η T (t)ψ τ<h η (t) α x(t), () for some scalar α > if Ψ τ<h Ω + τ(t)(p P ) Ω R Y T Z T (τ(t) h )Y T Ω Y T Z T (τ(t) h )Y T φ () S φ () φ ()
4 E. Fridman et al. / Automatica (9) (h τ(t))z T Ω 7 (h τ(t))z T Ω 7 T R + W S <, (7) (τ(t) h )T φ () (h τ(t))w ( τ(t))q + T + T T W (S + R ) where Ω j = AT P j + P T j A + S R, [ τ(t) Ω = h P + h τ(t) P P T h h + AT P, Ω j = P j P T + j (h i+ h i ) R i, i= Ω j 7 = Y T j Z T j + P T j A, Ω j 7 = Y T j Z T j + P T j A, φ () = (S + R S Q ), φ () = (S + R S ), φ () = ( )(τ(t) h )R, φ () = ( )(h τ(t))r, i, j =,. (8) The latter LMI leads for τ(t) h and for τ(t) h to the following LMIs: Ω + τ(t)(p P ) Ω R τ(t)=h Y T Z T Ω Y T Z T φ () Ψ = S φ () ( )Z T Ω 7 ( )Z T Ω 7 T R + W S <, (9) φ () (h τ(t)=h h )W ( τ(t))q + T + T T W (S + R ) and Ω + τ(t)(p P ) Ψ = Ω τ(t)=h R Y T Z T Ω Y T Z T φ () S φ () ( )Y T Ω 7 ( )Y T Ω 7 T R + W S <. () φ () (h τ(t)=h h )T ( τ(t))q + T + T T W (S + R ) It is easy to see that Ψ results from Ψ τ<h,τ=h, where we have deleted the zero row and the zero column. Denoting: η i (t) = col{x(t), ẋ(t), x(t h ), x(t h ), v ji, x(t τ(t)), x(t h )}, i =,, the latter two LMIs imply () because h τ(t) η T h h (t)ψ η (t) + τ(t) h η T h h (t)ψ η (t) = η T (t)ψ τ<h η (t) α x(t) and Ψ τ<h is thus convex in τ(t) [h, h ). LMI (9) leads for τ(t) = d i, i =, to the following: Ψ i = Ψ τ(t)=di <, i =,. () The two LMIs () imply (9) because d τ(t) d d Ψ + τ(t) d d d Ψ = Ψ <. and Ψ is thus convex in τ(t) [d, d. Similarly, we can obtain that Ψ is also convex in τ(t) [d, d. For τ(t) (h, h, where χ =, we apply the above arguments and representations with j = and i =,. Similarly to (), we insert free-weighting n n-matrices T, W, Y k, Z k (k =, ) by adding the following expressions to V : = [x T (t)y T + ẋt (t)y T + xt (t τ(t))t T + xt (t h )W T [ x(t h ) + x(t τ(t)) + (τ(t) h )v, = [x T (t)z T + ẋt (t)z T [x(t h ) + (h τ(t))v x(t τ(t)). Similarly to (), the expression with j = is added to V. We then arrive at the following: V τ>h η T (t)ψ τ>h η (t), where Ψ τ>h Ω + τ(t)(p P ) Ω R Y T (τ(t) h )Y T Ω Y T (τ(t) h )Y T φ () R W T + S (τ(t) h )W T φ () φ () (h τ(t))z T Ω 7 Z T (h τ(t))z T Ω 7 Z T W T T S <, () (τ(t) h )T φ () ( τ(t))q + T + T T S and where [ τ(t) Ω = h P + h τ(t) P φ () = (S + R + R S Q ), φ () = (S + R S ), φ () = ( )(τ(t) h )R, φ () = ( )(h τ(t))r. P T + AT P, () We note that Ψ τ>h is convex in τ(t) (h, h and, thus, for the feasibility of LMI (), it is sufficient to verify this LMI for τ(t) h and for τ(t) h. Denote the resulting LMIs by
5 7 E. Fridman et al. / Automatica (9) 7 77 Ψ < and Ψ <, respectively, where the zero columns and rows are deleted from Ψ and Ψ. Clearly Ψ and Ψ are also convex in τ(t) [d, d. Along the system (), we therefore have V τ h χ [h,h (τ(t))η T (t)ψ τ<h η (t) + [ χ [h,h (τ(t))η T (t)ψ τ>h η (t) α x(t) () for some positive scalar α >. For τ = h, taking into account the definition (7) of V, we find V τ=h max{η T (t)ψ τ<h η (t), η T (t)ψ τ>h η (t)} α x(t). () By using Theorem 8.. of (Kolmanovskii & Myshkis, 999), we finally obtain the following: Theorem. Let there exist n n-matrices Q, R i (i =,, ), S, S, S, S, satisfying (), and n n-matrices P k >, k =,,, W, W, P j, P j, Y j, Y j, T j, Z j and Z j, j =, such that the eight LMIs: (7), for τ(t) h and τ(t) h, and (), for τ(t) h and τ(t) h, where τ(t) = d, d, with notations given in (8) and (), are feasible. Then () is asymptotically stable for all differentiable delays τ(t) [h, h with d τ(t) d. For unknown d, by substituting P = P = P = P and τ(t) = d into (7) and (), we arrive at the following: Corollary. Let there exist n n-matrices Q, R i (i =,, ), S, S, S, S, satisfying (), and n n-matrices P >, W, W, P j, P j, Y j, Y j, T j, Z j and Z j, j =, such that the four LMIs: (7), for τ(t) h and τ(t) h, and (), for τ(t) h and τ(t) h, where τ(t) = d, with notations given in (8) and (), are feasible. Then () is asymptotically stable for all differentiable delays τ(t) [h, h with τ(t) d. Moreover, if the above LMIs are feasible with Q =, then () is asymptotically stable for all fastvarying delays in [h, h... On other possibilities for delay partitioning If h a is big enough, delay partitioning of [, h a can improve the result. For simplicity we combine delay partitioning of [, h a with a non-partitioned [h a, h b, where h a = h and h b = h. We apply V(t, x t, ẋ t ) = x T (t)p(τ(t))x(t) x(s) ( + t h x s h ) S S T ( x(s) S x s h ) ds + h ẋ T (s)r ẋ(s)dsdθ h t+θ h h + x T (s)s x(s)ds + x T (s)qx(s)ds t h t τ(t) h + ( ) ẋ T (s)r ẋ(s)dsdθ, () h t+θ where τ(t) [h, h and where P(τ(t)) = τ(t) h P + h τ(t) P, P >, P >, (7) S S Q, R >, R >, S >, >. (8) S We have: d dt [xt (t)p(τ(t))x(t) = x T (t) τ(t)(p P ) x(t) [ τ(t) + ẋ T h (t) P + h τ(t) P x(t). By using arguments of Theorem (without partitioning of [h a, h b ), we obtain that for some α > V η T (t)φη(t) α x(t), (9) where η(t) = col{x(t), ẋ(t), x(t h ), x(t h ), v, v, x(t τ(t)), x(t h )}, if the LMI Φ + τ(t)(p P ) Φ Y T Z T (τ(t) h )Y T Φ Y T Z T (τ(t) h )Y T S S + Q Φ = S Φ (h τ(t))z T Y T Z T + P T A S + R (h τ(t))z T Y T Z T + P T A T S T (τ(t) h )T Φ ( τ(t))q + T + T T S S R holds, where Φ = A T P + P T A + S R, [ τ(t) h Φ = P + h τ(t) P P T h h + AT P, Φ = P P T + h R + ( ) R, Φ = ( )(τ(t) h )R, Φ = ( )(h τ(t))r. The following result is then obtained. < () () Theorem. Let there exist n n-matrices Q, R, S, S, S, R, S, satisfying (8), and n n-matrices P >, P >, P, P T, Y, Y, Z, Z such that the four LMIs: (), for τ(t) h and τ(t) h, where τ(t) = d, d, with notations given in (), are feasible. Then () is asymptotically stable for all differentiable delays h τ(t) h satisfying d τ(t) d. When d is unknown, by setting P = P = P, τ(t) = d in (), we obtain the following Corollary. Let there exist n n-matrices Q, R, S, S, S, R, S, satisfying (8), and n n-matrices P >, P, P T, Y, Y, Z, Z such that the two LMIs: (), for τ(t) h and τ(t) h, where τ(t) = d, with notations given in (), are feasible. Then () is asymptotically stable for all differentiable delays h τ(t) h satisfying τ(t) d. Moreover, if the above LMIs are feasible with Q =, then () is asymptotically stable for all fast-varying delays in [h, h. Remark. The examples below illustrate that for big enough h a (for big enough h b h a ) the delay partitioning of [, h a (of [h a, h b ) improve the result. Thus, in Example, the results by Corollary are worse for h a and better for h a than the ones by Corollary. Partitioning of the above intervals into n > subintervals may lead to further improvements. In (Jiang & Han, 8) another delay partitioning was introduced, which corresponded to the partitioning into two subintervals of [, h a and of [, h b. Example below shows that our approach yields less conservative results.
6 E. Fridman et al. / Automatica (9) Table Example : Max. value of h b achieved for h a =. d \ d....7 unkn. Theorem Theorem Theorem Theorem Theorem Theorem Theorem Theorem Theorem Theorem Table Example : Max. value of h b for h a =. d \ Method He7 Shao9 Corollary Corollary..... unknown Table Example : Max. value of h b achieved for h a =. d \ d.... Theorem Theorem Theorem Theorem Examples Example. Consider () with A = and A =. For h a =, choosing d and d as in Table and applying Theorems and, we find the maximum values of h b for which the system remains asymptotically stable (see Table ). For unknown d, our results coincide with those of the corresponding Corollaries and. The result of Corollary coincides with the one of Park and Ko (7) (the latter are less conservative than those of He et al. (7)and Shao (9)), but the LMIs of Corollary possess a fewer number of decision variables. It is seen that the value of h b depends on d and it grows for d. For h a =, d unknown and d =. or unknown, the results obtained by various methods in the literature for the admissible upper-bounds h b, which guarantee the stability of the system () are listed in Table. For h a =, choosing d and d and applying Theorems and, we obtain the results given in Table. Example. Consider () with A = and A.9 =. For h a = we find, by applying Corollary, that the system is asymptotically stable for all fast-varying delays τ(t) [,.88, which coincides with the result of Park and Ko (7) (the latter is less conservative than those of He (7), Jiang and Han (8) and Shao (9)). Corollary leads to a bigger interval τ(t) [,.8. Table Example : Max. value of h b for different h a. h a Jiang and Han (8) Shao (9) Corollary Corollary Table Example : Max. value of h b achieved for d =. h a \ d..7 unknown Theorem Theorem For h a =,,,, and fast-varying delays we obtain, by applying Corollaries and, the maximum values of h b given in Table. These results are favorably compared with the existing ones. For d =, choosing d and h a as in Table we apply Theorems and. The results by Theorem are d -dependent (see Table ), where the value of h b grows for d. For unknown d the results coincide with those of Corollary. The results by Theorem are d -independent and coincide with the ones by Corollary.. Conclusions In this paper new LKFs with matrices depending on the time delay are introduced. These delay partitioning-based LKFs lead to stability conditions that depend on both the upper and lower bounds on the delay derivative. Two examples illustrate the efficiency of the new method and the improvement that can be achieved by using the lower bound on the delay derivative. Acknowledgements We thank the associate editor and the reviewers for their suggestions, which have improved the quality of the paper. References Fridman, E., & Shaked, U. (). A descriptor approach to H control of linear time-delay systems. Institute of Electrical and Electronics Engineers. Transactions on Automatic control, 7(), 7. Gouaisbaut, F., & Peaucelle, D. (). Delay-dependent stability of time delay systems. In: Proc. of ROCOND, oulouse. Gu, K., Kharitonov, V., & Chen, J. (). Stability of time-delay systems. Boston: Birkhauser. Hale, J., & Lunel, S. (99). Introduction to functional differential equations. New York: Springer-Verlag. He, Y., Wang, Q.-G., Lin, C., & Wu, M. (7). Delay-range-dependent stability for systems with time-varying delay. Automatica,, 7 7. Jiang, X., & Han, Q.-L. (8). New stability criteria for linear systems with interval time-varying delay. Automatica,, 8 8. Kolmanovskii, V., & Myshkis, A. (999). Applied theory of functional differential equations. Kluwer. Niculescu, S. I. (). Lecture Notes in Contr. and Inf. Sciences: Vol. 9. Delay effects on stability: A Robust Control Approach. London: Springer-Verlag. Park, P., & Ko, J. W. (7). Stability and robust stability for systems with a time-varying delay. Automatica,, Richard, J.-P. (). Time-delay systems: An overview of some recent advances and open problems. Automatica, 9, 7 9. Shao, H. (9). New delay-dependent criteria for systems with interval delay. Automatica,, 7 79.
Research 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 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 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 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 informationTHE phenomena of time delays are often encountered in
0 American Control Conference on O'Farrell Street San Francisco CA USA June 9 - July 0 0 Robust stability criteria for uncertain systems with delay and its derivative varying within intervals Luis Felipe
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 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 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 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 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 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 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 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 informationAsymptotic stability of solutions of a class of neutral differential equations with multiple deviating arguments
Bull. Math. Soc. Sci. Math. Roumanie Tome 57(15) No. 1, 14, 11 13 Asymptotic stability of solutions of a class of neutral differential equations with multiple deviating arguments by Cemil Tunç Abstract
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 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 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 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 informationThis 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 education use, including for instruction at the authors institution
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 informationThis article was published in an Elsevier journal. The attached copy is furnished to the author for non-commercial research and education use, including for instruction at the author s institution, sharing
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 informationStability Analysis of Linear Systems with Time-Varying Delays: Delay Uncertainty and Quenching
Proceedings of the 46th IEEE Conference on Decision and Control New Orleans, LA, USA, Dec. 2-4, 2007 Stability Analysis of Linear Systems with Time-Varying Delays: Delay Uncertainty and Quenching Antonis
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 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 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 informationThis 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 informationThis 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 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 informationNETWORKED control systems (NCS), that are comprised
1 Event-Triggered H Control: a Switching Approach Anton Selivanov and Emilia Fridman, Senior Member, IEEE Abstract Event-triggered approach to networked control systems is used to reduce the workload of
More informationResearch Article On Exponential Stability Conditions of Descriptor Systems with Time-Varying Delay
Applied Mathematics Volume 2012, Article ID 532912, 12 pages doi:10.1155/2012/532912 Research Article On Exponential Stability Conditions of Descriptor Systems with Time-Varying Delay S. Cong and Z.-B.
More informationThis 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 informationA novel control scheme for teleoperation with guaranteed performance under time-varying delays
A novel control scheme for teleoperation with guaranteed performance under time-varying delays Bo Zhang, Alexandre Kruszewski, Jean-Pierre Richard To cite this version: Bo Zhang, Alexandre Kruszewski,
More informationThis 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 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 informationInput-output framework for robust stability of time-varying delay systems
Input-output framework for robust stability of time-varying delay systems Yassine Ariba, Frédéric Gouaisbaut To cite this version: Yassine Ariba, Frédéric Gouaisbaut. Input-output framework for robust
More informationON THE ROBUST STABILITY OF NEUTRAL SYSTEMS WITH TIME-VARYING DELAYS
ON THE ROBUST STABILITY OF NEUTRAL SYSTEMS WITH TIME-VARYING DELAYS V. J. S. Leite P. L. D. Peres E. B. Castelan S. Tarbouriech UnED Divinópolis CEFET-MG R. Monte Santo, 319 35502-036, Divinópolis - MG
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 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 informationIntroduction to Time-Delay Systems. Emilia FRIDMAN
Introduction to Time-Delay Systems Emilia FRIDMAN 1 Models with time-delay and effects of delay on stability 2 A brief history of Time-Delay System (TDS) 3 Solution concept, the step method and the state
More information(This is a sample cover image for this issue. The actual cover is not yet available at this time.)
(This is a sample cover image for this issue. The actual cover is not yet available at this time.) This article appeared in a journal published by Elsevier. The attached copy is furnished to the author
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 informationStability of linear systems with general sawtooth delay
IMA Journal of Matematical Control an Information Page of 8 oi:0.093/imamci/nq03 Stability of linear systems wit general sawtoot elay KUN LIU, VLADIMIR SUPLIN AND EMILIA FRIDMAN Department of Electrical
More informationThis 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 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 informationThis 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 informationThis 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 informationAnalysis of Systems with State-Dependent Delay
Analysis of Systems with State-Dependent Delay Matthew M. Peet Arizona State University Tempe, AZ USA American Institute of Aeronautics and Astronautics Guidance, Navigation and Control Conference Boston,
More informationStabilization of Neutral Systems with Saturating Control Inputs
Stabilization of Neutral Systems with Saturating Control Inputs Joâo Manoel Gomes da Silva, Alexandre Seuret, Emilia Fridman, Jean-Pierre Richard To cite this version: Joâo Manoel Gomes da Silva, Alexandre
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 informationThis 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 informationThis 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 informationThis 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 informationAutomatica. Sliding mode control in the presence of input delay: A singular perturbation approach. X. Han a,1, E. Fridman b, S.K.
Automatica ( ) Contents lists available at SciVerse ScienceDirect Automatica journal homepage: www.elsevier.com/locate/automatica Brief paper Sliding mode control in the presence of input delay: A singular
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 informationThis 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 informationThis 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 informationRobust Stability Analysis of Teleoperation by Delay-Dependent Neutral LMI Techniques
Applied Mathematical Sciences, Vol. 8, 2014, no. 54, 2687-2700 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.42139 Robust Stability Analysis of Teleoperation by Delay-Dependent Neutral
More informationThis 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 informationDelay and Its Time-derivative Dependent Robust Stability of Uncertain Neutral Systems with Saturating Actuators
International Journal of Automation and Computing 74, November 200, 455-462 DOI: 0.007/s633-00-0527-3 Delay and Its ime-derivative Dependent Robust Stability of Uncertain Neutral Systems with Saturating
More informationThis article was published in an Elsevier journal. The attached copy is furnished to the author for non-commercial research and education use, including for instruction at the author s institution, sharing
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 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 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 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 information(This is a sample cover image for this issue. The actual cover is not yet available at this time.)
(This is a sample cover image for this issue. The actual cover is not yet available at this time.) This article appeared in a journal published by Elsevier. The attached copy is furnished to the author
More informationThis 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 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 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 informationNorm invariant discretization for sampled-data fault detection
Automatica 41 (25 1633 1637 www.elsevier.com/locate/automatica Technical communique Norm invariant discretization for sampled-data fault detection Iman Izadi, Tongwen Chen, Qing Zhao Department of Electrical
More informationDesign of Unknown Input Functional Observers for Delayed Singular Systems with State Variable Time Delay
WSEAS TRANSACTONS on SYSTEMS and CONTROL M. Khadhraoui M. Ezzine H. Messaoud M. Darouach Design of Unknown nput Functional Observers for Delayed Singular Systems State Variable Time Delay M. Khadhraoui
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 informationResearch Article Mean Square Stability of Impulsive Stochastic Differential Systems
International Differential Equations Volume 011, Article ID 613695, 13 pages doi:10.1155/011/613695 Research Article Mean Square Stability of Impulsive Stochastic Differential Systems Shujie Yang, Bao
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 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 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 informationMin Wu Yong He Jin-Hua She. Stability Analysis and Robust Control of Time-Delay Systems
Min Wu Yong He Jin-Hua She Stability Analysis and Robust Control of Time-Delay Systems Min Wu Yong He Jin-Hua She Stability Analysis and Robust Control of Time-Delay Systems With 12 figures Authors Min
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 informationLinear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay
Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay S. Lakshmanan and P. Balasubramaniam Department of Mathematics, Gandhigram Rural University,
More informationStability of neutral delay-diœerential systems with nonlinear perturbations
International Journal of Systems Science, 000, volume 1, number 8, pages 961± 96 Stability of neutral delay-diœerential systems with nonlinear perturbations JU H. PARK{ SANGCHUL WON{ In this paper, the
More informationTime-delay feedback control in a delayed dynamical chaos system and its applications
Time-delay feedback control in a delayed dynamical chaos system and its applications Ye Zhi-Yong( ), Yang Guang( ), and Deng Cun-Bing( ) School of Mathematics and Physics, Chongqing University of Technology,
More informationConstructing Lyapunov-Krasovskii Functionals For Linear Time Delay Systems
Constructing Lyapunov-Krasovskii Functionals For Linear Time Delay Systems Antonis Papachristodoulou, Matthew Peet and Sanjay Lall Abstract We present an algorithmic methodology for constructing Lyapunov-Krasovskii
More information(This is a sample cover image for this issue. The actual cover is not yet available at this time.)
This is a sample cover image for this issue. The actual cover is not yet available at this time.) This article appeared in a journal published by Elsevier. The attached copy is furnished to the author
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 informationOptimal nonlinear control for time delay system. Delsys 2013
. Optimal. (International nonlinear control for timeworkshop delay system Delsys November 22th, 2013) 1 / 21 Optimal nonlinear control for time delay system Liliam Rodríguez-Guerrero, Omar Santos and Sabine
More informationThis article was published in an Elsevier journal. The attached copy is furnished to the author for non-commercial research and education use, including for instruction at the author s institution, sharing
More informationDecentralized Disturbance Attenuation for Large-Scale Nonlinear Systems with Delayed State Interconnections
Decentralized Disturbance Attenuation for Large-Scale Nonlinear Systems with Delayed State Interconnections Yi Guo Abstract The problem of decentralized disturbance attenuation is considered for a new
More informationThis 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 informationImproved Stability Criteria for Lurie Type Systems with Time-varying Delay
Vol. 37, No. 5 ACTA ATOMATICA SINICA May, 011 Improved Stability Criteria for Lurie Type Systems with Time-varying Delay RAMAKRISHNAN Krishnan 1 RAY Goshaidas 1 Abstract In this technical note, we present
More informationExponential stability of families of linear delay systems
Exponential stability of families of linear delay systems F. Wirth Zentrum für Technomathematik Universität Bremen 28334 Bremen, Germany fabian@math.uni-bremen.de Keywords: Abstract Stability, delay systems,
More information20-Apr-2009, 15:21. The conference website can be found at
This is a preprint of an article accepted for presentation at POSTA 09 Third Multidisciplinary International Symposium on Positive Systems: Theory and Application c 2009 Springer. The conference website
More informationResearch Article Robust Tracking Control for Switched Fuzzy Systems with Fast Switching Controller
Mathematical Problems in Engineering Volume 212, Article ID 872826, 21 pages doi:1.1155/212/872826 Research Article Robust Tracking Control for Switched Fuzzy Systems with Fast Switching Controller Hong
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 informationThis 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 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 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 informationObserver-based sampled-data controller of linear system for the wave energy converter
International Journal of Fuzzy Logic and Intelligent Systems, vol. 11, no. 4, December 211, pp. 275-279 http://dx.doi.org/1.5391/ijfis.211.11.4.275 Observer-based sampled-data controller of linear system
More informationStability Analysis of Discrete-time Systems with Poisson-distributed Delays
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
More informationON THE GLOBAL STABILITY OF A NEUTRAL DIFFERENTIAL EQUATION WITH VARIABLE TIME-LAGS
Bulletin of athematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 9 Issue 4(2017), Pages 31-41. ON THE GLOBAL STABILITY OF A NEUTRAL DIFFERENTIAL EQUATION WITH VARIABLE
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 information