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Sliding Mode Control of Uncertain Parameter-Switching Hybrid Systems by Xiaojie Su, Peng Shi, Ligang Wu

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9Control of Switched Stochastic Hybrid Systems: Continuous-Time Case

9.1 Introduction

Stochastic systems play an important role in many branches of science and engineering applications, thus they have received much attention during recent decades. Many results reported about stochastic systems can be found in the literature, for example, stochastic stability analysis, stabilization, optimal and robust control, filtering, and model reduction. Recently, a great deal of work has been reported on stochastic systems with Markovian switching. These results motivate us to study some interesting topics on stochastic systems whose parameters operate by a switching signal, that is, the switched stochastic hybrid systems. This work is interesting and challenging since this kind of hybrid system integrates the switched hybrid systems into that of the stochastic systems, and thus is theoretically significant.

In this chapter, we investigate the control (including state feedback control and DOF control) problems for continuous-time switched stochastic hybrid systems. The average dwell time approach combined with the piecewise Lyapunov function technique are applied to derive the main results. There are two main advantages of using this approach to the switched system. First, this approach uses a mode-dependent Lyapunov function, which avoids some conservativeness caused by using a common Lyapunov ...

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