H2 and H∞ robust filtering for discrete-time linear systems

This paper investigates robust filtering design problems in H₂ and H_∞ spaces for discrete-time systems subjected to parameter uncertainty which 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 converted into convex programming problems written in terms of 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 guaranteed performance H₂ and H_∞ filters are proven to be of the same order as the order of the system. Some numerical examples illustrate the theoretical results