Tracking control for switched linear systems with time‐delay: a state‐dependent switching method

Tracking control for switched linear systems with time‐delay is investigated in this paper. Based on the state‐dependent switching method, sufficient conditions for the solvability of the tracking control problem are given. We use single Lyapunov function technique and a typical hysteresis switching law to design a tracking control law such that the H∞ model reference tracking performance is satisfied. The controller design problem can be solved efficiently by using linear matrices inequalities. Since convex combination techniques are used to derive the delay independent criteria, some subsystems are allowed to be unstable. It is highly desirable that a non‐switched time‐delay system can not earn such property. Simulation example shows the feasibility and validity of the switching control law. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

[1]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[2]  William E. Schmitendorf,et al.  Methods for Obtaining Robust Tracking Control Laws , 1986, 1986 American Control Conference.

[3]  B. R. Barmish,et al.  Robust asymptotic tracking for linear systems with unknown parameters , 1986, Autom..

[4]  A. Morse,et al.  Applications of hysteresis switching in parameter adaptive control , 1992 .

[5]  M. Mahmoud,et al.  Design of robust controllers for time-delay systems , 1994, IEEE Trans. Autom. Control..

[6]  G. Papavassilopoulos,et al.  Biaffine matrix inequality properties and computational methods , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[7]  Seizo Fujii,et al.  Adaptive switching control method and its application to tracking control of a robot , 1996, Proceedings of the 1996 IEEE IECON. 22nd International Conference on Industrial Electronics, Control, and Instrumentation.

[8]  Erik I. Verriest,et al.  Stability and Control of Time-delay Systems , 1998 .

[9]  Y. Cao,et al.  Delay-dependent robust stabilization of uncertain systems with multiple state delays , 1998, IEEE Trans. Autom. Control..

[10]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[11]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

[12]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[13]  Bo Hu,et al.  Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach , 2001, Int. J. Syst. Sci..

[14]  Bor-Sen Chen,et al.  Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model , 2001, IEEE Trans. Fuzzy Syst..

[15]  K. Gu,et al.  On robust stability of time-delay systems with norm-bounded uncertainty , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[16]  Bruce A. Francis,et al.  Stabilizing a linear system by switching control with dwell time , 2002, IEEE Trans. Autom. Control..

[17]  Jianliang Wang,et al.  Reliable robust flight tracking control: an LMI approach , 2002, IEEE Trans. Control. Syst. Technol..

[18]  Emilia Fridman,et al.  A descriptor system approach to H∞ control of linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[19]  João Pedro Hespanha,et al.  Postprints from CCDC Title Hysteresis-based switching algorithms for supervisory control of uncertain systems Permalink , 2002 .

[20]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[21]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[22]  Fen Wu,et al.  Switching LPV control designs using multiple parameter-dependent Lyapunov functions , 2004, Autom..

[23]  Guo-Ping Liu,et al.  Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties , 2004, IEEE Transactions on Automatic Control.

[24]  H. Özbay,et al.  STABILITY ANALYSIS OF SWITCHED TIME-DELAY SYSTEMS , 2005 .

[25]  S. Ge,et al.  Switched Linear Systems: Control and Design , 2005 .

[26]  Long Wang,et al.  Stabilization of switched linear systems with time-delay in detection of switching signal , 2005 .

[27]  Xinzhi Liu,et al.  Stability of a class of linear switching systems with time delay , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[28]  Jun Zhao,et al.  Stability and L2-gain analysis for switched delay systems: A delay-dependent method , 2006, Autom..

[29]  Qingwei Chen,et al.  Robust reliable control of switched uncertain systems with time-varying delay , 2006, Int. J. Syst. Sci..

[30]  Kok Lay Teo,et al.  Optimal control of switched systems with time delay , 2006, Appl. Math. Lett..

[31]  Peng Shi,et al.  $H_\infty$ Filtering of Discrete-Time Switched Systems With State Delays via Switched Lyapunov Function Approach , 2007, IEEE Transactions on Automatic Control.

[32]  Jun Zhao,et al.  On stability, L2-gain and Hinfinity control for switched systems , 2008, Autom..

[33]  D. Xie,et al.  Observer-based switched control design for switched linear systems with time delay in detection of switching signal , 2008 .

[34]  Jun Zhao,et al.  Robust tracking control for switched linear systems with time-varying delays , 2008, 2008 American Control Conference.

[35]  Sehjeong Kim,et al.  Delay independent stability of linear switching systems with time delay , 2008 .

[36]  Gou Nakura.  Noncausal Optimal Tracking of Linear Switched Systems , 2008, HSCC.