Sliding Mode Control of Uncertain Parameter-Switching Hybrid Systems

11State Estimation and SMC of Switched Stochastic Hybrid Systems

11.1 Introduction

In Chapter 9, we studied the problems of stability, stabilization, and control for the continuous-time switched stochastic hybrid system. In this chapter, we are interested in investigating the SMC design problem for such hybrid systems, and some results developed in Chapter 9 will be used. First, by designing an integral switching function, we obtain the sliding mode dynamics, which is a switched stochastic hybrid system with the same order as the original systems. Based on the stability analysis result in Chapter 9, a sufficient condition for the existence of the sliding mode is proposed in terms of LMIs, and an explicit parametrization of the desired switching function is also given. Then, a discontinuous SMC law for reaching motion is synthesized, such that the state trajectories of the SMC system can be driven onto a prescribed sliding surface and maintained there for all subsequent time. Moreover, considering that some system state components may not be available in practical applications, we further consider the state estimation problem by designing an observer. Sufficient conditions are also established for the existence and the solvability of the desired observer, and then the observer-based SMC law is synthesized.

11.2 System Description and Preliminaries

Consider the switched stochastic ...