Sliding Mode Control of Uncertain Parameter-Switching Hybrid Systems

8SMC of Switched State-Delayed Hybrid Systems: Discrete-Time Case

8.1 Introduction

In this chapter, we will study the SMC design problem for discrete-time switched hybrid systems with time-varying delay. First, we transform the original system into a new one with regular form, and then by designing a linear switching function, a reduced-order sliding mode dynamics, described by a switched state-delayed hybrid system, is generated. By utilizing the average dwell time approach and the piecewise Lyapunov function technique, a delay-dependent sufficient condition for the existence of the desired sliding mode is proposed in terms of LMIs, and an explicit parametrization of the desired switching surface is also given. Here, to reduce the conservativeness induced by the time delay in the system, both the slack matrix technique and the delay partitioning method are employed, which makes the proposed existence condition less conservative and more practical. The delay partitioning – also called delay fractioning – has been considered as an effective approach to reduce the conservativeness of the stability condition for time-delay systems. This was initially proposed by Gouaisbaut and Peaucelle in [86], and was then developed in [58, 73, 220, 271]. The basic idea of the delay partitioning method is to evenly partition the time delay into several components (this generally means time-invariant delay), and then take each time-delay component into account individually when constructing a ...