Stability of Time-Delay Feedback Switched Linear Systems

We address stability of state feedback switched linear systems in which delays are present in both the feedback state and the switching signal of the switched controller. For switched systems with average dwell-time switching signals, we provide a condition, in terms of upper bounds on the delays and in terms of a lower bound on the average dwell-time, to guarantee asymptotic stability of the closed loop. The condition also implies that, in general, feedback switched linear systems are robust with respect to both small state delays and small switching delays. Our approach combines existing multiple Lyapunov function techniques with the merging switching signal technique, which gives relationships between the average dwell times of two mismatched switching signals and their mismatched times. A methodology for numerical solution based on linear matrix inequality is also included.

I. Introduction

The focus of this work is to address stability of feedback switched systems in the presence of both state delays and switching delays (for background on switched systems, the reader is referred to [1] and the references therein). By a feedback switched system, we mean a switched plant connected in closed loop with a switched feedback controller.