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

ABSTRACT 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 and switching output-feedback control syntheses are proposed in terms of bilinear matrix 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 linear matrix 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 a min-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.