A LMI approach to H _∞ output feedback control for polytopic linear parameter-varying systems

This paper reviews the problem of H _∞, output feedback control for polytopic linear parameter-varying systems. It is different from those approaches which some matrices describing the system must be assumed to be constant and/or must satisfy structural constraints. In this paper, all the system matrices are assumed to be in a polytope and be affected by the parameters measured online, and there are no structural constraints. By employing the definition of Quadratic H _∞ Performance, sufficient conditions in terms of linear matrix inequalities are presented for the existence of the desired controller for the continuous linear parameter-varying system. The conditions guarantee that the closed-loop system is quadratically stable and with a prescribed H _∞ attenuation level. The proposed approach is potentially less conservative than previous ones for the plants without structural constraints. The numerical examples illustrate the effectiveness of the proposed approach.