ℋ∞-filtering design for discrete-time Markov Jump Systems with hidden parameters

In this paper we tackle the ℋ
_∞
filtering problem for a discrete-time Markov Jump Linear System (MJLS) with hidden parameters. We consider a hidden Markov model (θ(k); θ̂(k)) in which θ(k) is not accessible and corresponds to the mode of operation of the system, while θ̂(k) is a signal coming from a detector. The signal θ̂(k) acts as an estimation of θk) 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 θ̂(k) is proposed and the problem of obtaining an upper bound of the ℋ
_∞
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.