Gain-scheduled H_(2)/H_(∞)filtering for linear discrete-time systems with polytopic uncertainties

The design of the gain-scheduled H_(2)/H_(∞)filter for polytopic discrete-time systems is investigated.By introducing additional slack variables,a new mixed H_(2)/H_(∞)performance criterion is proposed,which provides a decoupling between the Lyapunov matrix and system matrices.Based on the new performance criterion,a sufficient condition for the existence of the gain-scheduled H_(2)/H_(∞)filter is derived.Furthermore,the filter design problem is converted into a convex optimization problem with linear matrix inequality(LMI)constraints.Simulation results show the effectiveness of the proposed approach.