H-2 and H-infinity robust filtering for discrete-time linear systems

This paper investigates robust filtering design problems in H-2 and H-infin ity spaces for discrete-time systems subjected to parameter uncertainty whi ch is assumed to belong to a convex bounded polyhedral domain. It is shown that, by a suitable change of variables, both design problems can be conver ted into convex programming problems written in terms of linear matrix ineq ualities (LMI). The results generalize the ones available in the literature to date in several directions. First, all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured. Then, assuming the order of the uncertain system is known, the optimal gua ranteed performance H-2 and H-infinity filters are proven to be of the same order as the order of the system. Comparisons with robust filters for syst ems subjected to norm-bounded uncertainty are provided in both theoretical and practical settings. In particular, it is shown that under the same assu mptions the results here are generally better as far as the minimization of a guaranteed cost expressed in terms of H-2 or H-infinity norms is conside red. Some numerical examples illustrate the theoretical results.