Discrete control of stochastic Markov switching systems with Lévy noise

In this paper, a nonlinear stochastic Markov switching system with Lévy noise is considered, and its stability is investigated with the assistance of Lyapunov theory. Firstly, a sliding mode surface for the system is designed, and the mean square exponential stability of sliding mode dynamics is verified. Moreover, it is proved that the system state can converge from the initial state to the sliding mode surface. After discretising the continuous controller, it is demonstrated that the second moment of the difference is bounded between the system states under the discrete controller and the continuous controller. Next, the stability of the system under the discrete controller is also ensured, and the maximum sampling interval that can maintain the stability of the discrete system is provided. Finally, simulation results indicate that the system maintains stability after the discretisation of the continuous controller.