Optimal filtering schemes for linear discrete-time systems: a linear matrix inequality approach

Abstract

This paper deals with the optimal filtering problem constrained to input noise signal corrupting the measurement output for linear discrete-time systems. The transfer matrix H(2) and/or H(infinity) norms are used as criteria in an estimation error sense. First, the optimal H(2) filtering gain is obtained from the H(2) norm state-space definition. Then the attenuation of arbitrary input signals is considered in an H(infinity) setting. Using the discrete-time version of the bounded real lemma on the estimation error dynamics, a linear stable filter guaranteeing the optimal H(infinity) attenuation level is achieved. Finally, the mixed H(2)/H(infinity) filter problem is solved, yielding a compromise between the preceding filter designs. All these filter design problems are formulated in a new convex optimization framework using linear matrix inequalites. A numerical example is presented.