Robust control for It ô stochastic systems with Markovian switching via sliding mode design

In this talk, the control problem of uncertain Itô stochastic systems with Markovian switching has been dealt with. A sliding mode control method is presented, in which the integral–type sliding function is utilized. By means of stochastic Lyapunov function, sufficient conditions via linear matrix inequalities (LMIs) with equality constraint are derived such that the sliding dynamics are stochastically stable with γ-disturbance attenuation. Moreover, the reachability of the specified sliding surface can be ensured. Especially, the designs of both sliding mode controller and sliding surface can be obtain via convex optimization.