H∞ control for Itô stochastic systems with markovian jump

In this paper, variable structure control for Itô stochastic systems with Markovian jump has been investigated. By means of linear matrix inequalities, the suitable sliding surfaces are given firstly. Then in order to guarantee that the sliding motions on the specified sliding surfaces are stochastically stable with some prescribed disturbance attenuation γ(>0), two theorems are given by Lyapunov-Krasovskii functionals. Finally, a simulation is provided to show the effectiveness and practicability of the proposed method.