Dissipative control for a class of polytopic LPV systems with a state delay

This note deals with the problem of dissipative control for a class of polytopic linear parameter-varying systems with a state delay. Based parameter-dependent Lyapunov approach, a dissipative criterion is given and then an improved condition is proposed by introducing a slack matrix. Moreover, using a polytopic characteristic of the dependent parameter, infinite dimensional linear matrix inequalities can be transformed into finite dimensional feasible problem, upon which gain-scheduled state feedback controller can be designed. The proposed controller can guarantee that the resulting closed-loop system is asymptotically stable and the given robust dissipative performance.