Exponential stabilization of LPV systems: An LMI approach

The design of robust observer-based output feedback controller that guarantees exponential stability for linear parameter varying (LPV) systems is considered in this paper. The synthesis problem is first formulated in terms of bilinear matrix inequalities (BMIs) and then sufficient linear matrix inequalities (LMIs) with equality constraint are provided to ensure exponential stability. The controller parameters are calculated efficiently using convex optimization techniques. The convergence rate of the closed loop system is also estimated. Furthermore, in the case of structured uncertainty, such as in the case of LPV systems, the proposed approach achieves less conservative results than that in the case of representing the uncertainty as a norm bounded one.