On the stability issues of switched singular time-delay systems with slow switching based on average dwell-time

Abstract

The issue of exponential stability analysis of continuous-time switched singular systems consisting of a family of stable and unstable subsystems with time-varying delay is investigated in this paper. It is very difficult to analyze the stability of such systems because of the existence of time-delay and unstable subsystems. In this regard, on the basis of the free-weighting matrix approach, by constructing the new Lyapunov-like Krasovskii functional, and using the average dwell-time approach, delay-dependent sufficient conditions are derived and formulated in terms of LMIs to check the exponential stability of such systems. This paper also highlights the relationship between the average dwell-time of the switched singular time-delay system, its stability, exponential convergence rate of differential states, and algebraic states. Finally, a numerical example is given to confirm the analytical results and illustrate the effectiveness of the proposed strategy. Copyright © 2012 John Wiley & Sons, Ltd. Copyright © 2012 John Wiley & Sons, Ltd.