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 H2 and/ or Hinfin; norms are used as criteria in an estimation error sense. First, the optimal filtering gain is obtained from the H 2 norm state-space definition. Then the attenuation of arbitrary input signals is considered in an H ∞ setting. Using the discrete-time version of the bounded real lemma on the estimation error dynamics, a linear stable filter guaranteeing the optimal H∞ attenuation level is achieved. Finally. the mixed H 2 / H∞ 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