Suboptimal reduced-order filtering through an LMI-based method

This paper addresses the reduced-order filtering design problem for continuous-time linear systems. The H₂ and H_infin norms of the estimation error, used as performance criteria, are discussed and a new linear matrix inequalities (LMI)-based method for reduced-order filter design is proposed. Differently from the methods available in the literature to date, the one presented here does not solve the associated nonconvex problem by means of an appropriate optimization procedure. It is based on the a priori determination of a certain matrix that simultaneously rends convex the problem to be solved and reduces the suboptimality degree of the solution. Its efficiency is tested by means of two examples. The first one, borrowed from the literature, allows the comparison of our method, for the H₂ norm case, with three earlier techniques, one of them being the well-known balanced truncation. The second one, of higher order, consists of the estimation of the displacement of a tapered bar using an H_infin norm criterion