H-2 and N-infinity robust filtering for convex bounded uncertain systems

This paper investigates robust filtering design problems in H-2 and H-infin ity spaces for continuous-time systems subjected to parameter uncertainty b elonging to a convex bounded-polyhedral domain. It is shown that, by a suit able change of variables, both designs can be converted into convex program ming problems written in terms of linear matrix inequalities. The results g eneralize the ones available in the literature to date in several direction s. 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 guaranteed performance H-2 and H -infinity filters are proven to be of the same order as the order of the sy stem. A numerical example illustrate the theoretical results.