Improved conditions for reduced-order 𠄋∞ filter design as a static output feedback problem

In this paper, the problem of reduced order H_∞ filter design for time-invariant discrete-time linear systems is investigated. The filtering problem is rewritten as a static output feedback control problem and the elimination lemma is applied to derive the design conditions for both precisely known and uncertain linear systems. An algorithm is proposed to solve the problem in two stages involving only linear matrix inequalities. A robust filter of arbitrary order is obtained by solving an optimization problem that minimizes an upper bound to the H_∞ performance of the estimation error dynamics. Numerical examples are presented to illustrate the advantages of the approach when compared to other techniques.