H∞-filtering for Markov jump linear systems with partial information on the jump parameter

We study in this work the H∞-filtering problem in a partial information context. We suppose that the state of the Markov chain θ(k) is not available to the filter, but only an estimation coming from a detector and represented by θ^(k). We present two main results related to the synthesis of filters that depend only on θ^(k) such that the H∞ norm in relation to the estimation error is limited: the case in which the transition and detection probabilities are not exactly known, but belong to distinct convex sets; and the Bernoulli case in which we derive necessary and sufficient conditions for the filter synthesis. All the results are given in terms of linear matrix inequalities and are illustrated by two numerical examples of systems prone to faults.