New stability criterion for linear switched systems with time‐varying delay

This paper studies the stability problem of a class of linear switched systems with time‐varying delay in the sense of Hurwitz convex combination. By designing a parameter‐dependent switching law and using a new convex combination technique to deal with delay terms, a new stability criterion is established in terms of LMIs, which is dependent on the parameters of Hurwitz convex combination. The advantage of the new criterion lies in its less conservatism and simplicity. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.

[1]  R. Decarlo,et al.  Construction of piecewise Lyapunov functions for stabilizing switched systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[2]  Raymond A. DeCarlo,et al.  Switched Controller Synthesis for the Quadratic Stabilisation of a Pair of Unstable Linear Systems , 1998, Eur. J. Control.

[3]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

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

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

[6]  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).

[7]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

[8]  Mohamed-Slim Alouini,et al.  Variable-rate noncoherent M-FSK modulation for power limited systems over Nakagami-fading channels , 2004, IEEE Transactions on Wireless Communications.

[9]  Shengyuan Xu,et al.  Improved delay-dependent stability criteria for time-delay systems , 2005, IEEE Transactions on Automatic Control.

[10]  Vu Ngoc Phat,et al.  Robust stability and stabilizability of uncertain linear hybrid systems with state delays , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[12]  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.

[13]  E. Boukas,et al.  DELAY-DEPENDENT STABILIZATION OF SINGULAR LINEAR SYSTEMS WITH DELAYS , 2006 .

[14]  Laurentiu Hetel,et al.  LMI control design for a class of exponential uncertain systems with application to network controlled switched systems , 2007, 2007 American Control Conference.

[15]  Lihua Xie,et al.  Further Improvement of Free-Weighting Matrices Technique for Systems With Time-Varying Delay , 2007, IEEE Transactions on Automatic Control.

[16]  Chung-Yao Kao,et al.  Stability analysis of systems with uncertain time-varying delays , 2007, Autom..

[17]  Yuanqing Xia,et al.  Design and Stability Criteria of Networked Predictive Control Systems With Random Network Delay in the Feedback Channel , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[18]  Qing-Long Han,et al.  A new delay-dependent absolute stability criterion for a class of nonlinear neutral systems , 2008, Autom..

[19]  Wei Wang,et al.  Stability Analysis for Linear Switched Systems With Time-Varying Delay , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  Guo-Ping Liu,et al.  Stability of Systems With Controller Failure and Time-Varying Delay , 2008, IEEE Transactions on Automatic Control.

[21]  Guo-Ping Liu,et al.  Delay-dependent stability for discrete systems with large delay sequence based on switching techniques , 2008, Autom..

[22]  Qing-Long Han,et al.  A discrete delay decomposition approach to stability of linear retarded and neutral systems , 2009, Autom..

[23]  Jun Zhao,et al.  Tracking control for switched linear systems with time‐delay: a state‐dependent switching method , 2009 .

[24]  Ge Guo,et al.  A switching system approach to actuator assignment with limited channels , 2009 .

[25]  Hisaya Fujioka.  Stability analysis of systems with aperiodic sample-and-hold devices , 2009, Autom..

[26]  Emilia Fridman,et al.  A refined input delay approach to sampled-data control , 2010, Autom..