H∞H∞ filtering for discrete-time linear systems with bounded time-varying parameters

In this paper, the problem of linear parameter varying (LPV) filter design for time-varying discrete-time polytopic systems with bounded rates of variation is investigated. The design conditions are obtained by means of a parameter-dependent Lyapunov function and extra variables for the filter design, expressed as bilinear matrix inequalities. An LPV filter, which minimizes an upper bound to the H∞H∞ performance of the estimation error, is obtained as the solution of an optimization problem. A convex model to represent the parameters and their variations as a polytope is proposed in order to provide less conservative design conditions. Robust filters for time-varying polytopic systems can be obtained as a particular case of the proposed method. Numerical examples illustrate the results.