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. © 2008 Elsevier Inc. All rights reserved.4301145154Anderson, B.D.O., Moore, J.B., (1979) Optimal Filtering, , Prentice-Hall, Englewood Cliffs, NJBarbosa, K.A., de Souza, C.E., Trofino, A., Robust H2 filtering for uncertain linear systems: LMI based methods with parametric Lyapunov functions (2005) Syst. Contr. Lett., 54 (3), pp. 251-262Boyd, S.P., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , SIAM, PhiladelphiaColaneri, P., Geromel, J.C., Locatelli, A., (1997) Control Theory and Design - An RH2 and RH∞ Viewpoint, , Academic Pressde Oliveira, M.C., Geromel, J.C., Hsu, L., LMI characterization of structural and robust stability: the discrete-time case (1999) Linear Algebra Appl., 296, pp. 27-38Geromel, J.C., Regis, L.A.V., H2 Optimal robust filtering (2006) Eur. J. Control, 12 (1), pp. 30-39Geromel, J.C., de Oliveira, M.C., Bernussou, J., Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions (2002) SIAM J. Control Optim., 41 (3), pp. 700-711Geromel, J.C., Optimal linear filtering under parameter uncertainty (1999) IEEE Trans. Signal Process., 47 (1), pp. 168-175Geromel, J.C., de Oliveira, M.C., Hsu, L., LMI characterization of structural and robust stability (1998) Linear Algebra Appl., 285, pp. 69-80Jain, B.N., Guaranteed error estimation in uncertain systems (1975) IEEE Trans. Automat. Contr., 20, pp. 230-232Li, L., Luo, Z.Q., Davidson, T.N., Wong, K.M., Bossé, E., Robust filtering via semidefinite programming with applications to target tracking (2002) SIAM J. Optim., 12 (3), pp. 740-755Marcos, S., A network of adaptive Kalman filters for data channel equalization (2000) IEEE Trans. Signal Process., 48 (9), pp. 2620-2627Martin, C.J., Mintz, M., Robust filtering and prediction for linear systems with uncertain dynamics: a game-theoretic approach (1983) IEEE Trans. Automat. Contr., 28 (9), pp. 888-896Poor, H.V., On robust Wiener filtering (1980) IEEE Trans. Automat. Contr., 25 (3), pp. 531-536Rockafellar, R., (1970) Convex Analysis, , Princeton PressShaked, U., Xie, L., Soh, Y.C., New approaches to robust minimum variance filter design (2001) IEEE Trans. Signal Process., 49 (11), pp. 2620-2629de Souza, C.E., Trofino, A., An LMI approach to the design of robust H2 filters (1999) Recent Advances on Linear Matrix Inequalities Methods in Control, , El Ghaoui L., and Niculescu S.-I. (Eds), SIAM, Englewood Cliffs, NJTheodor, Y., Shaked, U., Robust discrete-time minimum-variance filtering (1996) IEEE Trans. Signal Process., 44, pp. 181-189Tuan, H.D., Apkarian, P., Nguyen, T.Q., Robust and reduce-order filtering: new LMI-based characterizations and methods (2001) IEEE Trans. Signal Process., 49 (12), pp. 2975-2984L.H. Xie, Y.C. Soh, C. Du, Robust H2 estimation and control, Sch. Elect. Electron Eng., Nanyang Technol. Univ., Singapore, Tech. Rep., 1999Xie, L.H., Soh, Y.C., Robust Kalman filtering for uncertain systems (1994) Syst. Contr. Lett., 22, pp. 123-129Xie, L.H., Soh, Y.C., de Souza, C.E., Robust Kalman filtering for uncertain discrete-time systems (1994) IEEE Trans. Automat. Contr., 39, pp. 1310-131