State-Space Structure Of Finite Horizon Optimal Mixed ...Filter

. We show that in contrast to the infinite horizon case, the finite horizon optimal mixed H 2 =H 1 estimation problem has a bounded order solution. Moreover, when the underlying systems have state-space models of order n, the optimal finite horizon mixed H 2 =H 1 filter has state-space model of order no greater than 2n + 1. Similar results hold for mixed H 2 =H 1 control, though for brevity we shall only consider estimation problem here. Keywords. H 2 =H 1 theory, Convex optimization, State-space theory, Robust estimation. 1. INTRODUCTION In this paper we study the finite horizon mixed H 2 =H 1 estimation problem. In particular, we investigate the structure of the optimal mixed filter. The widely used H 2 theory dominated the classical estimation due to the fact that the optimal H 2 problem has a unique bounded order close-form solution with various desirable optimality properties. However, in the face of model uncertainties and lack of statistical information ..