H_∞ Filtering And Robust Stabilization For A Class Of Systems With Uncertainty

In this paper,we mainly consider the problem of reduced-order H_∞filtering and robust stabilization for a class of system with uncertainty. In the fist part of this paper,we solve the problem of reduced-order H_∞filtering for singular system with uncertainty.The purpose is to design linear filters with the order lower than the given system such that the filtering error system is regular, impluse-free, stable, and satisfies a prescribed H_∞performance level .One major contribution of this paper is that necessary and sufficient conditions for the solvability of this problem are obtained. These conditions are characterized in term of linear matrix inequalities(LMIs) and a coupling non-convex rank constranit.Moreover,an explicit parametrization of all desired reduced-order filters is obtained. In particular, when a static or zeroth-order H_∞filter is desired. It is shown that H_∞, filtering problem reduces to a convex LMI problem.In the second part ,we design a H_∞observer for a class of singular switching systems . By using the measure of the states,we can obtain the feedback laws and switching signal for the system. Moreover,we show that origin of the system is asymptotic stable under the given feedback laws and switching singal.In the third part, we consider the problem of asymptotic stablility for 2-switching systems. By using the polytopic-like Lyapunov function ,we solve the problem for the switching systems . we gain the sufficient condition of the problem and design the responding feedback laws and switching signal.