H2 Gain Scheduled Filtering for Polytopic Discrete-time Linear Parameter-Varying Systems

In this paper, the problem of H₂ filtering for polytopic discrete-time linear parameter-varying systems is studied. A gain scheduled filter, which not only can guarantee the filtering error system to be quadratically stable but also has a prescribed H₂ performance, is determined. The filter design is implemented by means of a convex optimization procedure and the time-varying parameters are supposed to affect all system matrices. Sufficient conditions are given for the existence of the desired filters from the solution of a linear matrix inequality problem formulated only in terms of the vertices of the polytope. A numerical example shows that the proposed filter design method is more effective and less conservative than some existing results.