A parameter-dependent Lyapunov function based design approach for gain-scheduled H∞ filters of LPV systems

In this paper we study the problem of designing gain-scheduled H∞ filters for a class of parameter-varying discrete-time systems. We utilize a parameter-dependent Lyapunov function to establish a new characterization of asymptotic stability with H∞ norm bound for the linear parameter-varying (LPV) systems. On the basis of the stability with H∞ performance characterization established, we provide sufficient conditions for the solvability of the filter design problem by means of a finite number of linear matrix inequalities (LMIs). Then we show that solving a set of LMIs paves the way for designing a desired gain-scheduled H∞ filter. We also use a numerical example to demonstrate the application of the presented filter design method.