Robust L∞ reliable control for uncertain nonlinear switched systems with time delay

This paper investigates the robust reliable L"~ control for a class of uncertain switched nonlinear systems with time delay. Firstly, L"~ performance condition for nonlinear switched system with time delay is proposed. Then, a sufficient condition of exponential stability with L"~ performance for switched system is given. Furthermore, a design methodology of the robust L"~ reliable control for switched nonlinear systems with time delay and parameter uncertainties is presented. The proposed state feedback controller, which guarantees exponential stability of closed-loop system, can be obtained using a set of linear matrix inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the main results.

[1]  Li Yu,et al.  An LMI approach to reliable guaranteed cost control of discrete-time systems with actuator failure , 2005, Appl. Math. Comput..

[2]  Zhengrong Xiang,et al.  Robust reliable control for uncertain switched nonlinear systems with time delay , 2008, WCICA 2008.

[3]  Shuzhi Sam Ge,et al.  Analysis and synthesis of switched linear control systems , 2005, Autom..

[4]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Short Survey of Recent Results , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..

[5]  Jamal Daafouz,et al.  Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach , 2002, IEEE Trans. Autom. Control..

[6]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[7]  David Angeli,et al.  Nonlinear norm-observability notions and stability of switched systems , 2005, IEEE Transactions on Automatic Control.

[8]  Bor-Sen Chen,et al.  L/sub /spl infin// - gain fuzzy control for nonlinear dynamic systems with persistent bounded disturbances , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[9]  Jun Zhao,et al.  GUARANTEED COST CONTROL FOR A CLASS OF UNCERTAIN SWITCHED DELAY SYSTEMS: AN AVERAGE DWELL-TIME METHOD , 2007, Cybern. Syst..

[10]  H. Antosiewicz,et al.  Differential Equations: Stability, Oscillations, Time Lags , 1967 .

[11]  Daniel Liberzon,et al.  Lie-Algebraic Stability Criteria for Switched Systems , 2001, SIAM J. Control. Optim..

[12]  Guangming Xie,et al.  Delay-dependent robust stability and Hinfinity control for uncertain discrete-time switched systems with mode-dependent time delays , 2007, Appl. Math. Comput..

[13]  A. Michel,et al.  Robust stabilizing control laws for a class of second-order switched systems , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[14]  João Pedro Hespanha,et al.  Uniform stability of switched linear systems: extensions of LaSalle's Invariance Principle , 2004, IEEE Transactions on Automatic Control.

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

[16]  S. Pettersson.  Observer Design for Switched Systems using Multiple Quadratic Lyapunov Functions , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..

[17]  Shouming Zhong,et al.  Delay-dependent stability of a type of linear switching systems with discrete and distributed time delays , 2008, Appl. Math. Comput..

[18]  Shaosheng Zhou,et al.  Generalized H2 output feedback controller design for uncertain discrete-time switched systems via switched Lyapunov functions , 2006 .

[19]  YUQIONG LIU,et al.  Reliable Control of Uncertain Nonlinear Systems , 1998, Autom..

[20]  Du Dongsheng,et al.  Robust H∞ output feedback controller design for uncertain discrete-time switched systems via switched Lyapunov functions , 2007 .

[21]  Daizhan Cheng,et al.  Stabilization of planar switched systems , 2004, Syst. Control. Lett..

[22]  Changlong Wang,et al.  Delay-dependent stability and stabilization of a class of linear switched time-varying delay systems , 2005, 2005 International Conference on Machine Learning and Cybernetics.

[23]  Wang Fu-zhong,et al.  LMI approach to reliable H ∞ control of linear systems , 2006 .

[24]  A. Morse,et al.  Nonlinear switched systems with state dependent dwell-time , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[25]  Zhendong Sun,et al.  Combined stabilizing strategies for switched linear systems , 2006, IEEE Trans. Autom. Control..

[26]  Long Wang,et al.  Robust stability analysis and control synthesis for discrete-time uncertain switched systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[27]  Lei Guo,et al.  STABILIZATION OF SWITCHED LINEAR SYSTEMS , 2003, IEEE Trans. Autom. Control..

[28]  Long-Yeu Chung,et al.  Robust reliable Hinfinity control for uncertain nonlinear systems via LMI approach , 2008, Appl. Math. Comput..

[29]  Ximing Sun,et al.  Exponential stability for switched delay systems based on average dwell time technique and Lyapunov function method , 2006, 2006 American Control Conference.

[30]  Zhang Lixian,et al.  Delay-dependent stability and stabilization of a class of linear switched time-varying delay systems.* , 2007 .

[31]  Xinzhi Liu,et al.  Stability of switched systems with time delay , 2007 .

[32]  Zhendong Sun.  A robust stabilizing law for switched linear systems , 2004 .

[33]  F. Sheikholeslam,et al.  Reliable H//sub/spl infin// control systems with uncertainties in all system matrices: an LMI approach , 2005, Proceedings of 2005 IEEE Conference on Control Applications, 2005. CCA 2005..

[34]  A. Stephen Morse,et al.  Switched nonlinear systems with state-dependent dwell-time , 2003, Syst. Control. Lett..