EXPONENTIAL STABILITY ANALYSIS AND STABILIZATION OF DISCRETE-TIME NONLINEAR SWITCHED SYSTEMS WITH TIME DELAYS

This note considers the problems of stability and stabilization for discretetime switched nonlinear systems with time-varying delay. The nonlinearity is assumed to satisfy a special constraint. The purpose of the robust stability problem is to give conditions such that the discrete-time switched nonlinear delay system is exponentially stable, while the purpose of stabilization is to design a state feedback control law such that the resulting closed-loop system is exponentially stable. By applying the average dwell time approach together with the piecewise Lyapunov function technique, also by constructing a proper Lyapunov-Krasovskii functional and employing the free-weighting matrix method, some delay-dependent stability conditions are proposed. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired state feedback control law is also given. Finally, two numerical examples are provided to demonstrate the application of the proposed methods.

[1]  W. McEneaney.  Robust/ H ∞ filtering for nonlinear systems , 1998 .

[2]  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).

[3]  Shengyuan Xu,et al.  Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay , 2001, Syst. Control. Lett..

[4]  Bo Hu,et al.  Disturbance attenuation properties of time-controlled switched systems , 2001, J. Frankl. Inst..

[5]  Bruce A. Francis,et al.  Stabilizing a linear system by switching control with dwell time , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

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

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

[8]  Huijun Gao,et al.  A delay-dependent approach to robust H∞ filtering for uncertain discrete-time state-delayed systems , 2004, IEEE Trans. Signal Process..

[9]  Guangming Xie,et al.  Quadratic Stabilization of Uncertain Discrete-Time Switched Systems via Output Feedback , 2005 .

[10]  J. Geromel,et al.  Stability and stabilization of discrete time switched systems , 2006 .

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

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

[13]  Yuan Gong Sun,et al.  Delay-dependent robust stability and stabilization for discrete-time switched systems with mode-dependent time-varying delays , 2006, Appl. Math. Comput..

[14]  Huijun Gao,et al.  New Results on Stability of Discrete-Time Systems With Time-Varying State Delay , 2007, IEEE Transactions on Automatic Control.

[15]  Guisheng Zhai,et al.  A Note on Multiple Lyapunov Functions and Stability Condition for Switched and Hybrid Systems , 2007, 2007 IEEE International Conference on Control Applications.

[16]  Ligang Wu,et al.  Sliding mode control of switched hybrid systems with time‐varying delay , 2008 .

[17]  Ligang Wu,et al.  Guaranteed cost control of switched systems with neutral delay via dynamic output feedback , 2009, Int. J. Syst. Sci..

[18]  Wei Xing Zheng,et al.  Weighted H∞ model reduction for linear switched systems with time-varying delay , 2009, Autom..

[19]  刘兴军,et al.  OBSERVER BASED MODEL REFERENCE OUTPUT FEEDBACK TRACKING CONTROL FOR SWITCHED LINEAR SYSTEMS WITH TIME DELAY CONSTANT DELAY CASE , 2010 .

[20]  Yurong Liu,et al.  A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances , 2010, Autom..

[21]  Lei Yu,et al.  DIRECT ADAPTIVE NEURAL CONTROL WITH SLIDING MODE METHOD FOR A CLASS OF UNCERTAIN SWITCHED NONLINEAR SYSTEMS , 2010 .