The robust finite-time control problems for linear discrete-time stochastic Markovian jump systems (MJSs) with external disturbance are investigated. Firstly, the definitions of robust finite-time boundedness, and robust finite-time boundedness are presented. Subsequently, by using the stochastic Lyapunov–Krasovskii functional method and linear matrix inequality technique, sufficient conditions for the existence of a robust finite-time controller are provided for stochastic MJSs. A state feedback controller is designed. Furthermore, the finite-time guaranteed cost bounds are given. More specifically, the designed controller not only ensures the finite-time bounded but also makes the cost function less than the bound given by the performance index of the systems. Finally, two examples are given to illustrate the validity of the proposed approach.
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