Sliding Mode Control of Uncertain Parameter-Switching Hybrid Systems

4SMC of Markovian Jump Singular Systems with Stochastic Perturbation

4.1 Introduction

In this chapter, we will investigate the SMC design problem for Markovian jump singular systems with stochastic perturbation. The stochastic perturbation considered here is described as a Brownian motion, thus the overall dynamics is actually governed by an Itô stochastic differential equation with Markovian switching parameters and singularity, namely a Markovian jump singular stochastic system. There have been some results reported on SMC of stochastic systems [155, 156, 158] and Markovian jump stochastic systems [157], but the SMC problem for a Markovian jump singular stochastic system has not been fully investigated and still remains challenging. Due to the stochastic perturbation, the stability analysis methods proposed in Chapters 2 and 3 are not fully applicable in this chapter. The commonly used method of analyzing the stability of stochastic systems is based on the Itô formula. In [23], Boukas proposed a sufficient stability condition for a Markovian jump singular stochastic system, but the results are not all of strict LMI form since there exist some matrix equality constraints, which may cause problems in checking the conditions numerically.

We shall design an appropriate integral sliding surface, taking the singular matrix E into account. As a result, the sliding mode dynamics, described by a Markovian jump singular stochastic system, can be easily derived. The order of the resulting ...