Sliding Mode Control Of Linear Switched Stochastic Delay Systems

Switching as an important control strategy has been widely used in various system models. The effect of switching on system dynamical behaviors has always been a hot topic in theory. In recent years, many important methods and remarkable achievements have been developed. However, most of these results are associated with switched systems with deterministic subsystems. Compared with deterministic systems, stochastic systems contain much more information, and are more reasonable to indicate the characteristic that engineering systems usually include random factors. In this thesis, a class of systems is studied, in which system dynamics is affected by stochastic disturbances, while the switching signal is still a deterministic function. By applying integral type sliding mode control, the stability for a class of switching signals satisfying average dwell time is investigated. The main results obtained in this thesis are as follows:The problem of sliding mode control for uncertain switched stochastic systems with time-varying delays is investigated. Construct an integral type sliding surface, and derive sufficient conditions in the form of linear matrix inequalities (LMIs) for mean-square exponential stability of the sliding mode dynamics by an average dwell time method. Then, variable structure controllers are designed to guarantee the system trajectories remain on the predefined sliding surface from the initial time.For generalized switched stochastic systems, the passivity-based sliding mode control under asynchronous switching is studied. According to the characteristics of asynchronous switching, the entire time interval is divided into two parts:unmatched periods and matched periods. An integral type sliding surface and a class of switching signals satisfying average dwell time are constructed. Sufficient conditions for mean-square exponential stability and stochastic passivity with dissipation rateγare developed. Moreover, variable structure controllers are designed to guarantee the reachability of the sliding surface.Considering a class of switched stochastic systems with unmeasurable states, the problem of observer-based sliding mode control under asynchronous switching is investigated. An observer is designed to estimate the system state. In addition, the design problem of an integral type sliding surface and variable structure controllers are considered when the switching signal of the observer lags behind that of the system. Meanwhile, sufficient conditions for mean-square exponential stability of the closed-loop system are developed. Finally, draw a conclusion of the results of the thesis, and point out some problems which deserve future study.