Stability and stabilization of switched linear dynamic systems with time delay and uncertainties

This paper considers the problem of exponential stability and stabilization of switched linear time-delay systems. The system parameter uncertainties are time-varying and unknown but norm-bounded. The delay in the system states is also time-varying. By using an improved Lyapunov-Krasovskii functional, a switching rule for the exponential stability and stabilization is designed in terms of the solution of Riccati-type equations. The approach allows for computation of the bounds that characterize the exponential stability rate of the solution. Numerical examples are given to illustrate the results.

[1]  Hai Lin,et al.  Switched Linear Systems: Control and Design , 2006, IEEE Transactions on Automatic Control.

[2]  F. Uhlig.  A recurring theorem about pairs of quadratic forms and extensions: a survey , 1979 .

[3]  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.

[4]  C. D. Souza,et al.  Robust exponential stability of uncertain systems with time-varying delays , 1998, IEEE Trans. Autom. Control..

[5]  G. Zhai,et al.  Quadratic stabilizability of switched linear systems with polytopic uncertainties , 2003 .

[6]  Ke Chen,et al.  Applied Mathematics and Computation , 2022 .

[7]  Guangming Xie,et al.  Quadratic stability and stabilization of discrete-time switched systems with state delay , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[8]  PooGyeon Park,et al.  A delay-dependent stability criterion for systems with uncertain time-invariant delays , 1999, IEEE Trans. Autom. Control..

[9]  Vu Ngoc Phat,et al.  Global stabilization for linear continuous time-varying systems , 2006, Appl. Math. Comput..

[10]  M. Parlakçi.  Improved robust stability criteria and design of robust stabilizing controller for uncertain linear time‐delay systems , 2006 .

[11]  Vladimir L. Kharitonov,et al.  Exponential estimates for retarded time-delay systems: an LMI approach , 2005, IEEE Transactions on Automatic Control.

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

[13]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.

[14]  Wanyi Chen,et al.  Some new results on the asymptotic stability of uncertain dynamical systems with time-varying delay , 2002, Int. J. Syst. Sci..

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

[16]  Yu Qiang Wu,et al.  Exponential stability of a class of switched and hybrid systems , 2004, ICARCV 2004 8th Control, Automation, Robotics and Vision Conference, 2004..

[17]  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..

[18]  Zhong-Ping Jiang,et al.  A switching algorithm for global exponential stabilization of uncertain chained systems , 2003, IEEE Trans. Autom. Control..

[19]  Guangming Xie,et al.  Stabilization of Switched Linear Systems with Multiple Time-Varying Delays , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[20]  Jinde Cao,et al.  Delay-dependent robust stability of uncertain nonlinear systems with time delay , 2004, Appl. Math. Comput..

[21]  V. Phat,et al.  Global stabilization of linear periodically time-varying switched systems via matrix inequalities , 2006 .

[22]  H. Abou-Kandil,et al.  Matrix Riccati Equations in Control and Systems Theory , 2003, IEEE Transactions on Automatic Control.