A new method to H2 robust filter design

In this paper a new method to H2 robust filter design is proposed. Both continuous and discrete time settings are considered for systems subject to polytopic parameter uncertainty. Lower and upper bounds of the true cost are determined in order to evaluate the degree of sub-optimality of the proposed robust filter. The design method is based on the parametrization of all robust filters as a convex combination of Kalman filters associated to each vertex of the uncertainty domain. Among all feasible filters, the one minimizing a guaranteed H2 cost of the estimation error is determined by a pure convex programming problem, expressed in terms of linear matrix inequalities (LMIs). The order of the robust filter is generally greater than the order of the plant, a fact that contributes to reduce conservatism. The proposed design technique is compared with other methods available in the literature. In several examples solved the proposed method outperforms all other designs.