Effects of Mixed-Modes on the Stability Analysis of Switched Time-Varying Delay Systems

A phenomenon, known as mixed-mode, occurs naturally in switched delay systems, and it makes the stability analysis for such systems a challenge, especially for the case of time-varying delays. This note aims to investigate the effects of mixed-modes on the stability analysis of switched time-varying delay systems, which are motivated from networked control applications. By constructing a Lyapunov-Krasovskii functional and using the estimation of quadrature, as well as the average dwell time approach, new exponential stability conditions are given for the switched time-varying delay systems with both stable and unstable subsystems. This can be seen as a generalization of existing results that mainly focus on the cases of constant delay and all stable subsystems. Finally, simulation examples are presented to illustrate the developed results.

[1]  Peng Shi,et al.  Stability and Stabilization of Switched Linear Systems With Mode-Dependent Average Dwell Time , 2012, IEEE Transactions on Automatic Control.

[2]  Dong Yue,et al.  A Delay System Method for Designing Event-Triggered Controllers of Networked Control Systems , 2013, IEEE Transactions on Automatic Control.

[3]  Wei Zhang,et al.  Stability of networked control systems , 2001 .

[4]  Stephen P. Boyd,et al.  Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization , 2005, Syst. Control. Lett..

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

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

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

[8]  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.

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

[10]  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).

[11]  Wen-an Zhang,et al.  Stabilization of Sampled-Data Control Systems With Control Inputs Missing , 2010, IEEE Transactions on Automatic Control.

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

[13]  Amir Hossein Davaie Markazi,et al.  Variable Selective Control Method for Networked Control Systems , 2013, IEEE Transactions on Control Systems Technology.

[14]  Huijun Gao,et al.  Asynchronously switched control of switched linear systems with average dwell time , 2010, Autom..

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

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