Stabilization And Observer Design Problem Of Swithed Systems

In this paper, we discuss the stabilization and observer design problem of switched systems. In the first part, we consider the stabilization of switched systems with controllable linear systems and the stabilization of its perturbation system when the perturbation term satisfies certain condition. For any given switching law, a feedback control can be designed to make the closed-loop system exponentially stable. In the second part, we consider the observer design and dynamic feedback problem of linear switched system with observable subsystems and the observer design of its perturbation systems. By constructing error systems, for any given switching law, observer matrices can be designed to make the error systems exponentially stable. In the third part, we consider the feedback stabilization of discrete-time switched system with controllable subsystems. For both cases of known and unknown finite switching frequency a linear feedback control can be constructed such that the closed-loop system is exponentially stable. Finally, using multiple Lyapunov functions, we discuss the stabilization of a class of nonlinear switched system. For a class of switching law, feedback control can be designed to make the closed-loop systems asymptotically stable.