H_∞ dynamic output feedback control for time-varying delay singular Markovian jump systems based on variable elimination technique

This paper deals with the dynamic output feedback H_∞ control problem for a kind of singular Markovian jump systems with time-varying delays. First, by utilizing improved Lyapunov-Krasovskii functional, sufficient conditions that singular Markovian jump systems with time varying delays satisfy stochastic admissibility are derived in terms of linear matrix inequalities. Second, a dynamic output feedback controller is constructed to ensure that the resulting closed-loop system satisfies stochastic admissibility and meets H_∞ performance index. Furthermore, non-convex inequalities are transformed into linear matrix inequalities by using variable elimination technique which is based on matrix transformation method. Finally, two numerical examples including direct-current motor driving a load model are given to prove the effectiveness and practicability of the main results obtained.