Robust switching output-feedback control of time-varying polytopic uncertain systems

The problem of designing a globally optimal robust output feedback controller for time-varying polytopic uncertain systems is a well-known non-convex optimisation problem. In this paper, new sufficient conditions for both robust H-2 and H-infinity switching output-feedback control syntheses are proposed in terms of bilinearmatrix inequalities (BMIs) under the multiple Lyapunov function framework. This set of synthesis conditions is further reduced to a special type of BMIs, which can be solved effectively using linearmatrix inequality optimisation plus a line search. The associated robust output-feedback controller is constructed as a switching-type full-order dynamic output-feedback controller, consisting of a family of linear time-invariant subcontrollers and amin-switching logic. The proposed approach features the important property of computational efficiency with stringent performance. Its effectiveness and advantages have been demonstrated through extensive numerical studies.