H∞ LPV Filtering for Linear Systems with Arbitrarily Time-varying Parameters in Polytopic Domains

In this paper, the problem of H_∞ filtering for linear systems affected by arbitrarily time-varying parameters in polytopic domains is investigated. A linear parameter-varying filter which minimizes an upper bound to the H_∞ estimation error performance is determined for both continuous and discrete-time cases. Different from other strategies in the literature, the filter design is accomplished by means of a convex optimization procedure and the time-varying parameters are supposed to affect all systems matrices. The LPV filter is obtained from the optimal solution of a convex linear matrix inequality problem formulated only in terms of the vertices of the polytope. There is no use of exhaustive gridding in the parameter space. Numerical examples illustrate the efficiency of the proposed approach