Delay-Dependent H∞ Control for Singular Markovian Jump Systems With Generally Uncertain Transition Rates

This article is devoted to the problem of $H_{\infty }$ control for a class of singular Markovian jump systems with time-varying delay and generally uncertain transition rates, which means each transition rate is completely unknown or only its estimated value is known. By using Lyapunov stability theory, a new delay-dependent $H_{\infty }$ admissible criterion in terms of strict linear matrix inequalities is obtained, which guarantees that the singular Markovian jump system with known transitions rates is regular, impulse-free and stochastically stable with a prescribed $H_{\infty }$ disturbance attenuation level $\gamma $ . Based on this obtained criterion, some suitable state feedback controllers are designed such that the closed-loop delayed singular Markovian jump system with generally uncertain transition rates is $H_{\infty }$ stochastically admissible. Finally, numerical examples are included to illustrate the effectiveness and the less conservativeness of the proposed method.