Sliding Mode Control of Uncertain Parameter-Switching Hybrid Systems

10Control of Switched Stochastic Hybrid Systems: Discrete-Time Case

10.1 Introduction

In this chapter, we will study the problems of stability and stabilization, and the control of discrete-time switched stochastic hybrid systems with time-varying delays. Similar to Chapter 9, the main results proposed in this chapter are obtained by employing the average dwell time approach and the piecewise Lyapunov function technique. However, the development of such methods in the continuous and discrete cases has certain technical differences. A sufficient condition, which guarantees the considered system mean-square exponentially stable, is first proposed in terms of LMIs, and by this the stabilization problem is then solved. The weighted performance condition is then also established, and control is designed. It is shown that the control problem can be converted into a convex optimization problem with a set of LMI constraints which can be solved by applying interior-point algorithms.

10.2 System Description and Preliminaries

Consider the discrete-time switched stochastic hybrid system ...