$H_{\infty }$ Filtering

Abstract

In this chapter, the problem of $H_{\infty }$ filtering for a class of discrete-time Markov jump linear systems (MJLSs) with partially unknown TPs is investigated. A mode-dependent full-order filter is constructed and the bounded real lemma (BRL) for the resulting filtering error system is derived via linear matrix inequality (LMI) formulation. Then, an improved version of the BRL is further given by introducing additional slack matrix variables to eliminate the cross coupling between system matrices and Lyapunov matrices among different operation modes. Finally, the existence criterion of the desired filter is obtained such that the corresponding filtering error system is stochastically stable with a guaranteed $H_{\infty }$ performance index.