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

In this paper, the robust H<sub>2</sub>/H<sub>∞</sub> 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<sub>2</sub> and H<sub>∞</sub> performance specifications. Sufficient conditions are derived, respectively, to ensure mean-square stability, the H<sub>2</sub> performance, and the H <sub>∞</sub> performance. A unified framework is established to solve the addressed robust H<sub>2</sub>/H<sub>∞</sub> 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<sub>2</sub>and H<sub>∞</sub> filtering performances. A numerical example is provided to illustrate the usefulness of the proposed method

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