Sability Analysis And Control For Stochastic Time Delay Switched Systems

Stochastic delay switched systems are hybrid systems with complex dynamic behaviors,because of the existence of time delay and switching. The study of stochastic delay switchedsystems is a popular topic and it has gained conservable research interests recently. This paperinvestigated stability and control for switched systems described by Ito stochastic differentialequation. Firstly, sufficient stability conditions are established based on average dwell timetechnique. Then conditions are presented in terms of linear matrices inequalities (LMIs). Then,based on the obtained stability criteria, the feedback controllers are designed. The issues, suchas finite-time stability, exponential stability, feedback control, guaranteed cost control andobserver-based control, are investigated. The effectiveness of the proposed methods isdemonstrated by numerical examples.The detailed contents of this thesis include:Based on the multiple Lyapunov function method and average dwell time technique,sufficient finite-time stability condition for stochastic delayed switched systems are presentedin the first part of this thesis. Then, a state feedback controller is designed to ensure the finitetime stability of the resulting closed-loop systems.The second part concerns with guaranteed cost control for stochastic delayed switchedsystems. By multiple Lyapunov function method, a guaranteed cost controller is designed,such that the cost function is not larger than an upper bound. And the optimal guaranteed costcontroller is determined by solving a set of linear matrices inequalities (LMIs).The third part focuses on the problem of observer-based controller design for stochasticdelayed switched systems. Based on the singular value decomposition technique, anobserver-based controller is developed, such that the closed-loop system is mean-squareexponentially stable with switching signal satisfying average dwell time requirement.