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In this paper, a sliding mode controller for time-delay Markovian jump systems with partly unknown transition probability matrix in presence of disturbance is designed. The proposed method is quite general and includes both systems with completely known and completely unknown transition probability rates. At first, sufficient conditions for existence of linear switching surface are obtained in terms of linear matrix inequalities (LMIs) that guarantee the stochastic stability of sliding mode dynamics. Then, a sliding mode controller is designed such that the closed-loop system’s state trajectories reach the desired sliding surface in a finite time and maintain there for all subsequent times. As a result, the stochastic stability of closed-loop system is guaranteed by applying a specifically designed control law. All of the conditions are presented in terms of linear matrix inequalities and can be simply solved by means of numerical software tools. Finally, a numerical example is given to demonstrate the validity and effectiveness of the proposed method.

Keywords: Markovian Jump Systems (MJSs), Stochastic Stability, Sliding Mode Control (SMC), Time-Delay, Partly Unknown Transition Probabilities, Linear Matrix Inequalities (LMIs).

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