Robust H₂/H_∞ Filtering for Uncertain Systems with Missing Measurement

Abstract

In this paper, the robust H ₂ /H _∞ filtering problem is addressed for a class of uncertain discrete-time stochastic systems with missing measurement. The purpose of this paper is to design a filter, such that for all possible missing measurement and admissible uncertainty, the filtering process is exponentially mean-square quadratically stable, and simultaneously achieves the prescribed H ₂ and H _∞ performance specifications. Sufficient conditions are derived, respectively, to ensure mean-square stability, the H ₂ performance, and the H _∞ performance. A unified framework is established to solve the addressed robust H ₂ /H _∞ filtering problem by using a linear matrix inequality (LMI) approach. As a by-product, two additional optimization problems are dealt with, aiming to optimize the H ₂ and H _∞ filtering performances. A numerical example is provided to illustrate the usefulness of the proposed method