H2 and Hoo Filtering of Discrete-Time Markov Jump Linear Systems through Linear Matrix Inequalities

This paper addresses the H2 and H∞ filtering design problems of discrete-time Markov jump linear systems. First, under the assumption that the Markov parameter is measured, the main contribution is on the LMI characterization of all filters such that the estimation error remains bounded by a given norm level, yielding the complete solution of the mode-dependent filtering design problem. Based on this result, a robust filter design to deal with convex bounded parameter uncertainty is considered. Second, from the same LMI characterization, a procedure for mode-independent filtering design is proposed. An example is solved for illustration and comparisons with the methods available in the literature.