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.