Sliding Mode Control of Uncertain Parameter-Switching Hybrid Systems

5Stability and Stabilization of Switched State-Delayed Hybrid Systems

5.1 Introduction

In the previous three chapters, we have solved SMC design problems for systems with Markovian switching parameters. From this chapter onward, we shall study the analysis and synthesis problems for another kind of parameter-switching systems, namely switched hybrid systems. In Chapter 1, we presented an overview of the recent developments in switched hybrid systems. The stability analysis problem for switched hybrid systems can be classified into two major categories: stability analysis under arbitrary switching and under restricted switchings. It was shown that switched systems may fail to preserve stability under arbitrary switching, but may be stable under restricted switching signals [131]. That is to say, the stability results under restricted switchings may have less conservativeness than those under arbitrary switching. Among the restricted switchings, the most famous concept is the average dwell time. In this book, we shall assume that the switching signal in the considered switched hybrid systems is not arbitrary, but is a restricted one having an average dwell time.

In this chapter, we shall investigate the stability analysis and stabilization problems for continuous- and discrete-time switched hybrid systems with time-varying delays. For continuous-time system, the time-varying delay d(t) is assumed to satisfy either (A1) 0 ≤ d(t) ≤ d and or (A2) 0 ≤ d(t) ≤ d. By using the average ...