Sliding Mode Control for a Class of Nonlinear Positive Markov Jumping Systems with Uncertainties in a Finite-time Interval

This paper studies the finite-time sliding mode control problem for a class of nonlinear positive Markov jumping systems with uncertain parameters. Firstly, a mode-dependent sliding mode surface is designed to guarantee the positiveness and finite-time boundedness of the closed-loop Markov jumping systems. Then, a suitable finite-time sliding mode controller is given to guarantee the closed-loop MJSs can drive onto the specified sliding mode surface during a given finite-time interval and then maintain on the sliding surface. Based on the stochastic Lyapunov-Krasovskii functional approach and linear matrix inequalities technique, sufficient conditions on the existence of the finite-time controller are proposed and proved. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.