H∞ filtering of time-varying systems with bounded rates of variation

In this paper, the problem of robust filter design for time-varying discrete-time polytopic systems with bounded rates of variation is investigated. The design conditions are obtained by using a parameter-dependent Lyapunov function and the Finsler´s Lemma. A robust filter, that minimizes an upper bound to the H_∞ performance of the estimation error, is obtained as the solution of an optimization problem. A more precise geometric representation of the parameter time variation was used in order to obtain less conservative design conditions. Robust filters for time-invariant, as well as arbitrarily time-varying, polytopic systems can be obtained as a particular case of the proposed method. Numerical examples illustrate the results.