Sliding Mode Control for the Generalized Markovian Jump System

The H_∞ tolerance of the generalized Markov jump system and the design of the sliding mode controller are studied. Firstly, a sliding mode surface is designed for the system, and then Liapunov function is introduced to obtain the linear matrix inequality for the H_∞ tolerance of the system, and the sufficient conditions for the tolerance of the system are obtained by the free power matrix method, the addition and subtraction terms, and the linear matrix inequality method. After that, the sliding mode dynamics is analyzed and a sliding mode controller is designed so that the system can be employed to reach the sliding mode surface in a finite time. Finally, the simulation results verify the effectiveness of the theory.