H∞ Admissibility of Singular Stochastic Systems with Markovian Switching and Partly Unknown Transition Rates

In this paper, we consider ${\mathcal{H}_\infty }$admissibility of singular stochastic systems with Markovian switching (SSMS) with partly unknown transition rates (PUTR). Until now, ${\mathcal{H}_\infty }$admissibility condition for SSMS have been studied for the limited cases: 1) SSMS which do not have a path from disturbances to the desired output, 2) the sufficient condition for the general SSMS. On the other hand, the authors successfully obtain the equivalent condition of ${\mathcal{H}_\infty }$admissibility criterion for SSMSs by introducing two slack variables. Also, because the proposed condition is expressed in terms of convex condition, i.e., linear matrix inequalities (LMIs), the result can be used to find the optimal ${\mathcal{H}_\infty }$performance even though the information about the transition rates is limited.