Robust Stabilization of the Uncertain Linear Systems. Based on Descriptor Form Representation t. Toru ASAI* and Shinji HARA**
|
|
- Darlene Stanley
- 5 years ago
- Views:
Transcription
1 Robust Stabilization of the Uncertain Linear Systems Based on Descriptor Form Representation t Toru ASAI* and Shinji HARA** This paper proposes a necessary and sufficient condition for the quadratic stabilization for a class of linear systems described by descriptor form representations. The system representation contains timevarying but bounded parameters representing the uncertainties. Similarly to the state-space form case, gives better performances as compared with the state-space method. 1. Introduction In recent years, robustness has been paid a lot of attention in control systems design. A lot of methods for the stabilization of systems with uncertainty have been proposed and efficient results have been achieved. Especially, a method of quadratic stabilization is one of powerful approaches for systems with the descriptor form is more suitable for the representation of real independent parametric Indeed, we can show that the descriptor uncertainties. form description is tighter than the state-space expression for representing real independent parametric perturbations. For example, let us consider a second order transfer function P(s) represented by bounded time-varying parametric uncertainties4),7)-9),14). The quadratic stabilization is based on the existence of a certain Lyapunov function of quadratic where T and K are assumed to be physical variables form which assures the global exponential and independent each other. A state-space representation asymptotic stability. It is well known that the qua- of P(s) is given by lem and the control law is constructed by solving a certain algebraic Riccati equation4). So far, the uncertainty have been considered based In the state space form, we have to consider the on the state-space form representation in the framework. perturbations of 1/T and K/T instead of T and K. However, in the process of modeling, a collec- Here, we have a question: Are there any differences tion of variables that is enough to describe the system between the perturbations of 1/T and K/T and those is defined and employed. Those variables generally of T and K? The answer is 'yes' and the difference have inherent meanings, or natural interpretations can be seen quite easily. Suppose that T and K vary within the context of the particular situation. Hence, over * Department of Control Engineering, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo ** Department of Systems Science, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama (Received May 31, 1994) (Reviced Octover 14, 1994) TR 0003/95/ (C) 1994 SICE
2 The change of 1/T is equivalent to that of T. However, the change of K/T denotes a sector with the In Sec. 3, we introduce the uncertain linear system necessary and sufficient condition are shown in Sec. 2. angle from tan-1 (KL/TH) to tan-1(kh/tl) on the (T, based on the descriptor form representation and K) parameter space. Therefore, the region covered establish the quadratic stabilization. The effectiveness of the proposed method is illustrated by an The regions covered by (1.3) and (1.4) are depicted in Fig. 1 shaded darkly and shallowly, respectively. As seen so far, the uncertainty is enlarged unnecessary by considering the uncertainty in the state-space form and this enlargement would cause, the conservativeness in the robust control system design. Therefore, it is necessary to consider the uncertainty of (T,K) independently in order to avoid the enlargement of the uncertainty. As a way to consider the parameters independently, we can employ the following system representation : (1.5) is known to be a descriptor form representation of P(s)13). Using descriptor form representation, we can separately consider the parameters like mass, time-constant, etc. from other parameters. From the point of view discussed above, we consider the uncertainty represented in the descriptor form and establish the robust stabilization. In this paper, we propose a method of quadratic stabilization based on the descriptor form representation with parameter uncertainties. The approach is similar to the state-space form case. In other words, the problem of the quadratic stabilization can be The definition of the quadratic stability and the example in Sec. 4. The proof of Theorem 2.1 uses several lemmas in Appendix. The notation used in this paper is standard. For a given matrix A, AT and A* denotes its transpose and its conjugate transpose, respectively. If all eigenvalues of a matrix lie on the open left half side of the complex plane, we call the matrix Hurwitz. If eigenvalues of A, respectively. For any vector x, x denotes the standard Euclidean norm of x. For any matrix G partitioned as the linear fractional transformation of a matrix K is given as 5,(G,K):=G11+G12K(I-G22K)-1G21 (1.7) where K must have compatible sizes. 2. Definitions and Preliminary Results The stability of the closed-loop system is established through the analysis-of a quadratic Lyapunov function. In order to introduce the notion of quadratic stability, we employ an autonomous timevarying system. Let us first consider an uncertain system J represented by representing the uncertainty and assumed to be Lebesgue measurable function such that PT(t)P(t)<_I;dt>0 (2.2) Fig. 1 Regions covered by the uncertainty of (T,K) and (1/T, K/T)
3 we can rewrite the above inequality as While many researcher have defined the quadratic stability for several uncertain linear systems4),9),7), we define the quadratic stability for a linear timeinvariant system with a bounded time-varying matrix. However, our definition is equivalent to that of Petersen et al.4),9),7), since our uncertain linear system includes those systems as special cases. easily checked by constructing output of the time-varying that. This fact is the system from the uncertainty to the input of If the inequality (2.3) is satisfied, it is straight forward to verify that the time-varying system J is uniformly, exponentially and asymptotically stable. The quadratic stability of the system J has a close relation to the small-gain theorem measured with the Proof: (Sufficiency) Consider the quadratic form V(x(t)):=xT(t)Px(t), where P is a positive definite matrix satisfying (A.1) in Appendix. The derivative of V(x(t)) is written by Furthermore, the bound is replaced with xtqx, where (Necessity) Suppose that the system J is quadratically stable. From the definition of the quadratic stability, (x,t): the following inequality holds for all pairs Since I-DTD is positive definite from Lemma A.3, Since the RHS of the above inequality is non-positive, we have the following inequality :
4 3. Main Result 3.1 Descriptor Form Representation As stated in the introduction, we want to robustly stabilize the uncertainty in the descriptor form. Firstly, let us consider a nominal plant with descriptor form representation expressed as vector, the control input and the output, respectively. Usually, in the context of the descriptor system, the matrix E is assumed to be singular in general. However, it is assumed in Sections 3.1, 3.2 and 3.3 that E is non-singular, since the focus is only on investigating the properties of the robust stability in terms of the representations of real parameters. A slight extension to the singular case will be briefly examined in Section 3.4. Corresponding to the above system representation, we consider a linear system described by the descriptor form equation:
5 ble iff there exists a linear time-invariant system K which satisfies the following two statements concerned as the closed-loop system Fl(G,K): (S1) The closed-loop system Fl(G,K) is internally stable. Fig. 3 Relations of system
6
7 4. Numerical Illustrations Here we illustrate the effectiveness of the stabilizing method proposed in the previous section. Let us consider a transfer function of a motor given by (1.1) and uncertain parameters (T,K) given by (1.3). The system is described in the descriptor form as (1.5). In order to express the perturbation of (T,K) with time-varying admissible uncertainties, let us Here we define GDF as the time-invariant (3.3) whose values are given by (4.4). On the other hand, in the state-space system is described as (1.2). (4.4) system form, the In this case, we must consider the perturbation of parameters (1/T, K/T) instead of (T,K). Let us define the time-varying
8 T. SICE Vol. 31 No. 8 August Conclusion A necessary and sufficient condition for the qua- dratic stabilization based on the descriptor form representation has been provided in this paper. It was shown that the stability of the system can be estab- References
9 Robust and Nonlin. Contr., 1, 153/169 (1991) 6) A. Packard and J. Doyle: Quadratic Stability with Real and Complex Perturbations, IEEE Trans., AC-35-2, 198/201 (1990) 7) I. R. Petersen: A Stabilization Algorithm for a Class of Uncertain Linear Systems, Syst. Contr. Lett., 8, 351/357 (1987) 8) I. R. Petersen: Stabilization of an Uncertain Linear System in which Uncertain Parameters Enter into the Input Matrix, SIAM J. Contr. Optimiz., 26-6, 1257/ 1264 (1988) 9) I. R. Petersen and C. V. Hollot: A Riccati Equation Approach to the Stabilization of Uncertain Linear Systems, Automatica, 22-4, 397/411 (1986) 11) T. Shiotsuki and S. Kawaji: A Model Reduction Algorithm of Descriptor Systems with Purely Static Part, Trans. of SICE, 24-10, 1056/1063 (1988) (In Japanese) 12) E. Uezato and M. Ikeda: Quadratic Stabilization of Linear Descriptor Systems, Preprints of the 16th SICE Symposium on Dynamical System Theory, 271/ 276 (1993) (In Japanese) 13) G. C. Verghese, B. C. Levy and T. Kailath: A Generalized State-space for Singular Systems, IEEE Trans., AC-26-4, 811/831 (1981) Lemma A. 4 Suppose that I-DTD>0 holds and that a positive definite matrix P is given. Then, for the system Y defined by (2.1), there exists an admissible uncertainty xt(t)pb(i-dtd)-1(w(t) satisfying the following equation: -DTz(t))
10 T. SICE Vol. 31 No. 8 August 1995 Also note that (A.11) and (A.12) imply Torn ASAI (Student Member) He received the B. E. and M. E. degrees in control engineering from Tokyo Institute of Technology, Tokyo, Japan, in 1991, and 1993, respectively. He is currently a doctor student in Tokyo Institute of Technology. His current research interests are in robust control theory and its application. Shinji HARA (Member)
Lyapunov 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 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 informationUniversity of Twente. Faculty of Mathematical Sciences. On stability robustness with respect to LTV uncertainties
Faculty of Mathematical Sciences University of Twente University for Technical and Social Sciences P.O. Box 17 75 AE Enschede The Netherlands Phone: +31-53-48934 Fax: +31-53-4893114 Email: memo@math.utwente.nl
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 informationStatic Output Feedback Stabilisation with H Performance for a Class of Plants
Static Output Feedback Stabilisation with H Performance for a Class of Plants E. Prempain and I. Postlethwaite Control and Instrumentation Research, Department of Engineering, University of Leicester,
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 informationFloor Control (kn) Time (sec) Floor 5. Displacement (mm) Time (sec) Floor 5.
DECENTRALIZED ROBUST H CONTROL OF MECHANICAL STRUCTURES. Introduction L. Bakule and J. Böhm Institute of Information Theory and Automation Academy of Sciences of the Czech Republic The results contributed
More informationHybrid Systems Course Lyapunov stability
Hybrid Systems Course Lyapunov stability OUTLINE Focus: stability of an equilibrium point continuous systems decribed by ordinary differential equations (brief review) hybrid automata OUTLINE Focus: stability
More informationDidier HENRION henrion
POLYNOMIAL METHODS FOR ROBUST CONTROL PART I.1 ROBUST STABILITY ANALYSIS: SINGLE PARAMETER UNCERTAINTY Didier HENRION www.laas.fr/ henrion henrion@laas.fr Pont Neuf over river Garonne in Toulouse June
More informationRobust SPR Synthesis for Low-Order Polynomial Segments and Interval Polynomials
Robust SPR Synthesis for Low-Order Polynomial Segments and Interval Polynomials Long Wang ) and Wensheng Yu 2) ) Dept. of Mechanics and Engineering Science, Center for Systems and Control, Peking University,
More informationIN THIS paper we will consider nonlinear systems of the
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 44, NO. 1, JANUARY 1999 3 Robust Stabilization of Nonlinear Systems Pointwise Norm-Bounded Uncertainties: A Control Lyapunov Function Approach Stefano Battilotti,
More informationTHE PARAMETERIZATION OF ALL ROBUST STABILIZING MULTI-PERIOD REPETITIVE CONTROLLERS FOR MIMO TD PLANTS WITH THE SPECIFIED INPUT-OUTPUT CHARACTERISTIC
International Journal of Innovative Computing, Information Control ICIC International c 218 ISSN 1349-4198 Volume 14, Number 2, April 218 pp. 387 43 THE PARAMETERIZATION OF ALL ROBUST STABILIZING MULTI-PERIOD
More informationRobust/Reliable Stabilization of Multi-Channel Systems via Dilated LMIs and Dissipativity-Based Certifications
19th Mediterranean Conference on Control and utomation quis Corfu Holiday Palace, Corfu, Greece June 2-23, 211 TuT1.5 Robust/Reliable Stabilization of Multi-Channel Systems via Dilated LMIs and Dissipativity-Based
More informationL 2 -induced Gains of Switched Systems and Classes of Switching Signals
L 2 -induced Gains of Switched Systems and Classes of Switching Signals Kenji Hirata and João P. Hespanha Abstract This paper addresses the L 2-induced gain analysis for switched linear systems. We exploit
More informationMapping MIMO control system specifications into parameter space
Mapping MIMO control system specifications into parameter space Michael Muhler 1 Abstract This paper considers the mapping of design objectives for parametric multi-input multi-output systems into parameter
More informationState feedback gain scheduling for linear systems with time-varying parameters
State feedback gain scheduling for linear systems with time-varying parameters Vinícius F. Montagner and Pedro L. D. Peres Abstract This paper addresses the problem of parameter dependent state feedback
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 informationADAPTIVE OUTPUT FEEDBACK CONTROL OF NONLINEAR SYSTEMS YONGLIANG ZHU. Bachelor of Science Zhejiang University Hanzhou, Zhejiang, P.R.
ADAPTIVE OUTPUT FEEDBACK CONTROL OF NONLINEAR SYSTEMS By YONGLIANG ZHU Bachelor of Science Zhejiang University Hanzhou, Zhejiang, P.R. China 1988 Master of Science Oklahoma State University Stillwater,
More informationLyapunov stability ORDINARY DIFFERENTIAL EQUATIONS
Lyapunov stability ORDINARY DIFFERENTIAL EQUATIONS An ordinary differential equation is a mathematical model of a continuous state continuous time system: X = < n state space f: < n! < n vector field (assigns
More informationA New Algorithm for Solving Cross Coupled Algebraic Riccati Equations of Singularly Perturbed Nash Games
A New Algorithm for Solving Cross Coupled Algebraic Riccati Equations of Singularly Perturbed Nash Games Hiroaki Mukaidani Hua Xu and Koichi Mizukami Faculty of Information Sciences Hiroshima City University
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 informationDerivation of Robust Stability Ranges for Disconnected Region with Multiple Parameters
SICE Journal of Control, Measurement, and System Integration, Vol. 10, No. 1, pp. 03 038, January 017 Derivation of Robust Stability Ranges for Disconnected Region with Multiple Parameters Tadasuke MATSUDA
More informationNonlinear Control Design for Linear Differential Inclusions via Convex Hull Quadratic Lyapunov Functions
Nonlinear Control Design for Linear Differential Inclusions via Convex Hull Quadratic Lyapunov Functions Tingshu Hu Abstract This paper presents a nonlinear control design method for robust stabilization
More informationQUANTITATIVE L P STABILITY ANALYSIS OF A CLASS OF LINEAR TIME-VARYING FEEDBACK SYSTEMS
Int. J. Appl. Math. Comput. Sci., 2003, Vol. 13, No. 2, 179 184 QUANTITATIVE L P STABILITY ANALYSIS OF A CLASS OF LINEAR TIME-VARYING FEEDBACK SYSTEMS PINI GURFIL Department of Mechanical and Aerospace
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 informationTHIS paper deals with robust control in the setup associated
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL 50, NO 10, OCTOBER 2005 1501 Control-Oriented Model Validation and Errors Quantification in the `1 Setup V F Sokolov Abstract A priori information required for
More informationMatrix Mathematics. Theory, Facts, and Formulas with Application to Linear Systems Theory. Dennis S. Bernstein
Matrix Mathematics Theory, Facts, and Formulas with Application to Linear Systems Theory Dennis S. Bernstein PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD Contents Special Symbols xv Conventions, Notation,
More informationSwitched systems: stability
Switched systems: stability OUTLINE Switched Systems Stability of Switched Systems OUTLINE Switched Systems Stability of Switched Systems a family of systems SWITCHED SYSTEMS SWITCHED SYSTEMS a family
More informationParameterized Linear Matrix Inequality Techniques in Fuzzy Control System Design
324 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 9, NO. 2, APRIL 2001 Parameterized Linear Matrix Inequality Techniques in Fuzzy Control System Design H. D. Tuan, P. Apkarian, T. Narikiyo, and Y. Yamamoto
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 informationFiltering for Linear Systems with Error Variance Constraints
IEEE RANSACIONS ON SIGNAL PROCESSING, VOL. 48, NO. 8, AUGUS 2000 2463 application of the one-step extrapolation procedure of [3], it is found that the existence of signal z(t) is not valid in the space
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 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 informationStability and Stabilizability of Switched Linear Systems: A Short Survey of Recent Results
Proceedings of the 2005 IEEE International Symposium on Intelligent Control Limassol, Cyprus, June 27-29, 2005 MoA01-5 Stability and Stabilizability of Switched Linear Systems: A Short Survey of Recent
More informationSimultaneous State and Fault Estimation for Descriptor Systems using an Augmented PD Observer
Preprints of the 19th World Congress The International Federation of Automatic Control Simultaneous State and Fault Estimation for Descriptor Systems using an Augmented PD Observer Fengming Shi*, Ron J.
More informationControl and Robustness for Quantum Linear Systems
CCC 2013 1 Control and Robustness for Quantum Linear Systems Ian R. Petersen School of Engineering and Information Technology, UNSW Canberra CCC 2013 2 Introduction Developments in quantum technology and
More informationA new method to obtain ultimate bounds and convergence rates for perturbed time-delay systems
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR ONTROL Int. J. Robust. Nonlinear ontrol 212; 22:187 188 ublished online 21 September 211 in Wiley Online Library (wileyonlinelibrary.com)..179 SHORT OMMUNIATION
More informationRobust Input-Output Energy Decoupling for Uncertain Singular Systems
International Journal of Automation and Computing 1 (25) 37-42 Robust Input-Output Energy Decoupling for Uncertain Singular Systems Xin-Zhuang Dong, Qing-Ling Zhang Institute of System Science, Northeastern
More informationRiccati difference equations to non linear extended Kalman filter constraints
International Journal of Scientific & Engineering Research Volume 3, Issue 12, December-2012 1 Riccati difference equations to non linear extended Kalman filter constraints Abstract Elizabeth.S 1 & Jothilakshmi.R
More informationSet-based adaptive estimation for a class of nonlinear systems with time-varying parameters
Preprints of the 8th IFAC Symposium on Advanced Control of Chemical Processes The International Federation of Automatic Control Furama Riverfront, Singapore, July -3, Set-based adaptive estimation for
More informationParametric Nevanlinna-Pick Interpolation Theory
Proc Natl Sci Counc ROC(A) Vol, No 6, 1998 pp 73-733 Parametric Nevanlinna-Pick Interpolation Theory FANG-BO YEH*, CHIEN-CHANG LIN**, AND HUANG-NAN HUANG* *Department of Mathematics Tunghai University
More informationAuxiliary signal design for failure detection in uncertain systems
Auxiliary signal design for failure detection in uncertain systems R. Nikoukhah, S. L. Campbell and F. Delebecque Abstract An auxiliary signal is an input signal that enhances the identifiability of a
More informationIntroduction to Nonlinear Control Lecture # 3 Time-Varying and Perturbed Systems
p. 1/5 Introduction to Nonlinear Control Lecture # 3 Time-Varying and Perturbed Systems p. 2/5 Time-varying Systems ẋ = f(t, x) f(t, x) is piecewise continuous in t and locally Lipschitz in x for all t
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 informationIndirect Model Reference Adaptive Control System Based on Dynamic Certainty Equivalence Principle and Recursive Identifier Scheme
Indirect Model Reference Adaptive Control System Based on Dynamic Certainty Equivalence Principle and Recursive Identifier Scheme Itamiya, K. *1, Sawada, M. 2 1 Dept. of Electrical and Electronic Eng.,
More information1030 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 56, NO. 5, MAY 2011
1030 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL 56, NO 5, MAY 2011 L L 2 Low-Gain Feedback: Their Properties, Characterizations Applications in Constrained Control Bin Zhou, Member, IEEE, Zongli Lin,
More informationarzelier
COURSE ON LMI OPTIMIZATION WITH APPLICATIONS IN CONTROL PART II.1 LMIs IN SYSTEMS CONTROL STATE-SPACE METHODS STABILITY ANALYSIS Didier HENRION www.laas.fr/ henrion henrion@laas.fr Denis ARZELIER www.laas.fr/
More informationFixed-Order Robust H Filter Design for Markovian Jump Systems With Uncertain Switching Probabilities
IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 54, NO. 4, APRIL 2006 1421 Fixed-Order Robust H Filter Design for Markovian Jump Systems With Uncertain Switching Probabilities Junlin Xiong and James Lam,
More informationConvergence Rate of Nonlinear Switched Systems
Convergence Rate of Nonlinear Switched Systems Philippe JOUAN and Saïd NACIRI arxiv:1511.01737v1 [math.oc] 5 Nov 2015 January 23, 2018 Abstract This paper is concerned with the convergence rate of the
More informationNonlinear Control. Nonlinear Control Lecture # 8 Time Varying and Perturbed Systems
Nonlinear Control Lecture # 8 Time Varying and Perturbed Systems Time-varying Systems ẋ = f(t,x) f(t,x) is piecewise continuous in t and locally Lipschitz in x for all t 0 and all x D, (0 D). The origin
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 informationH State-Feedback Controller Design for Discrete-Time Fuzzy Systems Using Fuzzy Weighting-Dependent Lyapunov Functions
IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL 11, NO 2, APRIL 2003 271 H State-Feedback Controller Design for Discrete-Time Fuzzy Systems Using Fuzzy Weighting-Dependent Lyapunov Functions Doo Jin Choi and PooGyeon
More informationOptimal Control of Linear Systems with Stochastic Parameters for Variance Suppression
Optimal Control of inear Systems with Stochastic Parameters for Variance Suppression Kenji Fujimoto, Yuhei Ota and Makishi Nakayama Abstract In this paper, we consider an optimal control problem for a
More informationAn efficient algorithm to compute the real perturbation values of a matrix
An efficient algorithm to compute the real perturbation values of a matrix Simon Lam and Edward J. Davison 1 Abstract In this paper, an efficient algorithm is presented for solving the nonlinear 1-D optimization
More informationLOW ORDER H CONTROLLER DESIGN: AN LMI APPROACH
LOW ORDER H CONROLLER DESIGN: AN LMI APPROACH Guisheng Zhai, Shinichi Murao, Naoki Koyama, Masaharu Yoshida Faculty of Systems Engineering, Wakayama University, Wakayama 640-8510, Japan Email: zhai@sys.wakayama-u.ac.jp
More informationRobust Internal Model Control for Impulse Elimination of Singular Systems
International Journal of Control Science and Engineering ; (): -7 DOI:.59/j.control.. Robust Internal Model Control for Impulse Elimination of Singular Systems M. M. Share Pasandand *, H. D. Taghirad Department
More informationStability of interval positive continuous-time linear systems
BULLETIN OF THE POLISH ACADEMY OF SCIENCES TECHNICAL SCIENCES, Vol. 66, No. 1, 2018 DOI: 10.24425/119056 Stability of interval positive continuous-time linear systems T. KACZOREK Białystok University of
More informationChapter III. Stability of Linear Systems
1 Chapter III Stability of Linear Systems 1. Stability and state transition matrix 2. Time-varying (non-autonomous) systems 3. Time-invariant systems 1 STABILITY AND STATE TRANSITION MATRIX 2 In this chapter,
More informationarxiv: v3 [math.oc] 1 Sep 2018
arxiv:177.148v3 [math.oc] 1 Sep 218 The converse of the passivity and small-gain theorems for input-output maps Sei Zhen Khong, Arjan van der Schaft Version: June 25, 218; accepted for publication in Automatica
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 informationTitle unstable additive/multiplicative pe. works must be obtained from the IEE
Title Robust stability of sampled-data sy unstable additive/multiplicative pe Author(s) Hagiwara, T; Araki, M Citation IEEE Transactions on Automatic Cont 346 Issue Date 998-09 URL http://hdl.handle.net/2433/39968
More informationOn robustness of suboptimal min-max model predictive control *
Manuscript received June 5, 007; revised Sep., 007 On robustness of suboptimal min-max model predictive control * DE-FENG HE, HAI-BO JI, TAO ZHENG Department of Automation University of Science and Technology
More informationResearch Article An Equivalent LMI Representation of Bounded Real Lemma for Continuous-Time Systems
Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 28, Article ID 67295, 8 pages doi:1.1155/28/67295 Research Article An Equivalent LMI Representation of Bounded Real Lemma
More informationOn Absolute Stability of Lur e Control Systems. with Multiple Nonlinearities
On Absolute Stability of Lur e Control Systems with Multiple Nonlinearities Min Wu a, Yong He a, Guo-Ping Liu b, Jin-Hua She c a School of Information Science and Engineering, Central South University,
More informationRobust Multivariable Control
Lecture 1 Anders Helmersson anders.helmersson@liu.se ISY/Reglerteknik Linköpings universitet Addresses email: anders.helmerson@liu.se mobile: 0734278419 http://users.isy.liu.se/rt/andersh/teaching/robkurs.html
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 informationIEEE Transactions on Automatic Control, 2013, v. 58 n. 6, p
Title Sufficient and Necessary LMI Conditions for Robust Stability of Rationally Time-Varying Uncertain Systems Author(s) Chesi, G Citation IEEE Transactions on Automatic Control, 2013, v. 58 n. 6, p.
More informationLecture 8. Applications
Lecture 8. Applications Ivan Papusha CDS270 2: Mathematical Methods in Control and System Engineering May 8, 205 / 3 Logistics hw7 due this Wed, May 20 do an easy problem or CYOA hw8 (design problem) will
More informationChapter Stability Robustness Introduction Last chapter showed how the Nyquist stability criterion provides conditions for the stability robustness of
Lectures on Dynamic Systems and Control Mohammed Dahleh Munther A Dahleh George Verghese Department of Electrical Engineering and Computer Science Massachuasetts Institute of Technology c Chapter Stability
More informationBackstepping Control of Linear Time-Varying Systems With Known and Unknown Parameters
1908 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL 48, NO 11, NOVEMBER 2003 Backstepping Control of Linear Time-Varying Systems With Known and Unknown Parameters Youping Zhang, Member, IEEE, Barış Fidan,
More informationSynthesis of Static Output Feedback SPR Systems via LQR Weighting Matrix Design
49th IEEE Conference on Decision and Control December 15-17, 21 Hilton Atlanta Hotel, Atlanta, GA, USA Synthesis of Static Output Feedback SPR Systems via LQR Weighting Matrix Design Jen-te Yu, Ming-Li
More informationPERIODIC signals are commonly experienced in industrial
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 15, NO. 2, MARCH 2007 369 Repetitive Learning Control of Nonlinear Continuous-Time Systems Using Quasi-Sliding Mode Xiao-Dong Li, Tommy W. S. Chow,
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 informationOptimization based robust control
Optimization based robust control Didier Henrion 1,2 Draft of March 27, 2014 Prepared for possible inclusion into The Encyclopedia of Systems and Control edited by John Baillieul and Tariq Samad and published
More informationResearch Article Robust Admissibilization of Descriptor Systems by Static Output-Feedback: An LMI Approach
Mathematical Problems in Engineering Volume 2011, Article ID 960981, 10 pages doi:10.1155/2011/960981 Research Article Robust Admissibilization of Descriptor Systems by Static Output-Feedback: An LMI Approach
More informationHybrid Systems - Lecture n. 3 Lyapunov stability
OUTLINE Focus: stability of equilibrium point Hybrid Systems - Lecture n. 3 Lyapunov stability Maria Prandini DEI - Politecnico di Milano E-mail: prandini@elet.polimi.it continuous systems decribed by
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 informationNonlinear Discrete-Time Observer Design with Linearizable Error Dynamics
622 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 48, NO. 4, APRIL 2003 Nonlinear Discrete-Time Observer Design with Linearizable Error Dynamics MingQing Xiao, Nikolaos Kazantzis, Costas Kravaris, Arthur
More informationDissipativity. Outline. Motivation. Dissipative Systems. M. Sami Fadali EBME Dept., UNR
Dissipativity M. Sami Fadali EBME Dept., UNR 1 Outline Differential storage functions. QSR Dissipativity. Algebraic conditions for dissipativity. Stability of dissipative systems. Feedback Interconnections
More informationLOCALLY POSITIVE NONLINEAR SYSTEMS
Int. J. Appl. Math. Comput. Sci. 3 Vol. 3 No. 4 55 59 LOCALLY POSITIVE NONLINEAR SYSTEMS TADEUSZ KACZOREK Institute of Control Industrial Electronics Warsaw University of Technology ul. Koszykowa 75 66
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 informationH 1 optimisation. Is hoped that the practical advantages of receding horizon control might be combined with the robustness advantages of H 1 control.
A game theoretic approach to moving horizon control Sanjay Lall and Keith Glover Abstract A control law is constructed for a linear time varying system by solving a two player zero sum dierential game
More informationDynamic Integral Sliding Mode Control of Nonlinear SISO Systems with States Dependent Matched and Mismatched Uncertainties
Milano (Italy) August 28 - September 2, 2 Dynamic Integral Sliding Mode Control of Nonlinear SISO Systems with States Dependent Matched and Mismatched Uncertainties Qudrat Khan*, Aamer Iqbal Bhatti,* Qadeer
More information1. Find the solution of the following uncontrolled linear system. 2 α 1 1
Appendix B Revision Problems 1. Find the solution of the following uncontrolled linear system 0 1 1 ẋ = x, x(0) =. 2 3 1 Class test, August 1998 2. Given the linear system described by 2 α 1 1 ẋ = x +
More informationA Recurrent Neural Network for Solving Sylvester Equation With Time-Varying Coefficients
IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL 13, NO 5, SEPTEMBER 2002 1053 A Recurrent Neural Network for Solving Sylvester Equation With Time-Varying Coefficients Yunong Zhang, Danchi Jiang, Jun Wang, Senior
More informationResearch Article Partial Pole Placement in LMI Region
Control Science and Engineering Article ID 84128 5 pages http://dxdoiorg/11155/214/84128 Research Article Partial Pole Placement in LMI Region Liuli Ou 1 Shaobo Han 2 Yongji Wang 1 Shuai Dong 1 and Lei
More informationUNCERTAINTY MODELING VIA FREQUENCY DOMAIN MODEL VALIDATION
AIAA 99-3959 UNCERTAINTY MODELING VIA FREQUENCY DOMAIN MODEL VALIDATION Martin R. Waszak, * NASA Langley Research Center, Hampton, Virginia Dominick Andrisani II, Purdue University, West Lafayette, Indiana
More informationGramians based model reduction for hybrid switched systems
Gramians based model reduction for hybrid switched systems Y. Chahlaoui Younes.Chahlaoui@manchester.ac.uk Centre for Interdisciplinary Computational and Dynamical Analysis (CICADA) School of Mathematics
More informationRobust fixed-order H Controller Design for Spectral Models by Convex Optimization
Robust fixed-order H Controller Design for Spectral Models by Convex Optimization Alireza Karimi, Gorka Galdos and Roland Longchamp Abstract A new approach for robust fixed-order H controller design by
More informationAny domain of attraction for a linear constrained system is a tracking domain of attraction
Any domain of attraction for a linear constrained system is a tracking domain of attraction Franco Blanchini, Stefano Miani, Dipartimento di Matematica ed Informatica Dipartimento di Ingegneria Elettrica,
More informationAPPROXIMATE SOLUTION OF A SYSTEM OF LINEAR EQUATIONS WITH RANDOM PERTURBATIONS
APPROXIMATE SOLUTION OF A SYSTEM OF LINEAR EQUATIONS WITH RANDOM PERTURBATIONS P. Date paresh.date@brunel.ac.uk Center for Analysis of Risk and Optimisation Modelling Applications, Department of Mathematical
More informationFEL3210 Multivariable Feedback Control
FEL3210 Multivariable Feedback Control Lecture 5: Uncertainty and Robustness in SISO Systems [Ch.7-(8)] Elling W. Jacobsen, Automatic Control Lab, KTH Lecture 5:Uncertainty and Robustness () FEL3210 MIMO
More informationFurther Results on Model Structure Validation for Closed Loop System Identification
Advances in Wireless Communications and etworks 7; 3(5: 57-66 http://www.sciencepublishinggroup.com/j/awcn doi:.648/j.awcn.735. Further esults on Model Structure Validation for Closed Loop System Identification
More informationRobust Tuning of Power System Stabilizers Using Coefficient Diagram Method
International Journal of Electrical Engineering. ISSN 0974-2158 Volume 7, Number 2 (2014), pp. 257-270 International Research Publication House http://www.irphouse.com Robust Tuning of Power System Stabilizers
More informationCHAPTER 5 ROBUSTNESS ANALYSIS OF THE CONTROLLER
114 CHAPTER 5 ROBUSTNESS ANALYSIS OF THE CONTROLLER 5.1 INTRODUCTION Robust control is a branch of control theory that explicitly deals with uncertainty in its approach to controller design. It also refers
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 informationContraction Based Adaptive Control of a Class of Nonlinear Systems
9 American Control Conference Hyatt Regency Riverfront, St. Louis, MO, USA June -, 9 WeB4.5 Contraction Based Adaptive Control of a Class of Nonlinear Systems B. B. Sharma and I. N. Kar, Member IEEE Abstract
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 informationThe Rationale for Second Level Adaptation
The Rationale for Second Level Adaptation Kumpati S. Narendra, Yu Wang and Wei Chen Center for Systems Science, Yale University arxiv:1510.04989v1 [cs.sy] 16 Oct 2015 Abstract Recently, a new approach
More informationDesign of Discrete-time Repetitive Control System Based on Two-dimensional Model
International Journal of Automation and Computing 9(2), April 212, 165-17 DOI: 1.17/s11633-12-629-1 Design of Discrete-time Repetitive Control System Based on Two-dimensional Model Song-Gui Yuan 1,2 Min
More information