The asynchronous observer-based finite-time control problem for discrete-time singular Markovian jump systems with time-varying delays is studied, where the asynchronism of the controller and observer with respect to the original system is fully taken into consideration. By the use of finite-time analysis theory and the construction of suitable Lyapunov-Krasovskii functionals, sufficient conditions to determine the closed-loop error system is singular stochastic finite-time boundedness are given with performance level. Then, by applying linear matrix inequalities, the desired observer parameters and controller parameters can be computed. Finally, the effectiveness of our proposed method is confirmed by simulation.
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