H_∞ filtering for singular Markovian jump systems with partly unknown transition rates

This paper suggests H_∞ filtering for singular Markovian jump systems (SMJSs) with partly unknown transition rates. While the existing researches in the literature have derived only the sufficient conditions, this paper successfully demonstrates the necessary and sufficient condition for the existence of H_∞ filtering for SMJSs with partly unknown transition rates. First, a new bounded real lemma for SMJS is derived in terms. Next, the matrix inequalities which come from the bounded real lemma for the filtering error system with partly unknown transition rates are reformulated into the strict LMIs. Two numerical examples are presented to show the effectiveness of the proposed result.