In this work, we consider the design of H∞ filters for semi-Markov jump systems with phase-type distributions and partial observation of the mode of operation. By means of a parametrization technique, we present design conditions for full-order H∞ filters in terms of linear matrix inequalities whose structure switch according to observations of the cluster type. By means of these results, we are able to design robust filter with respect to polytopic uncertainties in the plant. In order to illustrate our result, we present an academic application in the context of estimation of systems subject to faults.
