An LMI Approach to State Feedback H∞ Control for Switched Singular Linear System.s

In this paper, the problems of state feedback H-infinity control for a class of switched singular linear systems are investigated. By constructing a novel switched.Lyapunov functional and convex combinations techniques, a sufficient condition established in terms of strict linear matrix inequalities (LMIs) is presented such that the system is asymptotically stable and satisfies H-infinity performance. An explicit expression for the state feedback stabilization sub-controller and switching rule are designed. The merits of the proposed criteria lie in their less conservativeness and relative simplicity, in which the closed-loop system satisfies H-infinity performance at each point in whole state-space through switching, although each sub-system doesn't satisfy the performance and even is not asymptotically stable. A numerical example is provided to illustrate the validity of the proposed methods.