Mixed H2/H∞ filtering for Markov jump linear systems

We study in this work the mixed -filtering problem for Markov jump linear systems in a partial observation context. Rather than the Markov chain , we consider that only an estimation coming from a detector is available to the filter. We present a sufficient condition for the synthesis of a filter depending only on such that the estimation errors for the and filtering problems are bounded by given scalars. The robust mixed filtering considering that the transition and detection probabilities are uncertain, as well as the complete observation, cluster and mode-independent cases, are also studied. The results are given in terms of linear matrix inequalities and are illustrated by a numerical example.