H∞-Filtering Design for Discrete-Time Markov Jump Systems with Hidden Parameters

In this paper we tackle the H-infinity filtering problem for a discrete-time Markov Jump Linear System (MJLS) with hidden parameters. We consider a hidden Markov model (theta(k),theta(k)) in which theta(k) is not accessible and corresponds to the mode of operation of the system, while theta(k) is a signal coming from a detector. The signal theta(k) acts as an estimation of theta(k) and is the observable part of the hidden Markov model available to the filter. This approach generalizes several cases found in literature like the complete observation case, the mode independent case and the Markov models in fault-tolerant control. In this context, a new filter structure depending only on theta(k) is proposed and the problem of obtaining an upper bound of the H-infinity norm of the estimation error is studied. Sufficient conditions in terms of linear matrix inequalities (LMI) are given. The results are illustrated by a numerical example.