H2 and H∞ robust filtering for convex bounded uncertain systems

This paper investigates robust filtering design problems in H2 and H∞ spaces for continuous-time systems subjected to parameter uncertainty belonging to a convex bounded polyhedral domain. It is shown that, by a suitable change of variables, both designs can be converted into convex programming problems written as linear matrix inequalities (LMI). All system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured. Assuming the order of the uncertain system is known, the optimal guaranteed performance H2 and H∞ filters are proven to be of the same order as the order of the system. A numerical example illustrate the theoretical results.