Robust H∞ Control for Jump Systems Subject to Actuator Saturation

In order to solve the H_∞ control problem for a class of Markov jump systems subject to actuator saturation, a design method of the controllers is proposed Based on stochastic stability for the closed-loop system, H_∞ controller is designed. The concept of domain of attraction is used to analyze the stochastic stability and a sufficient condition which guarantees the intersection of ellipsoid invariant set under different modes in the domain of attraction is presented. The solvability condition of robust H_∞ controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal H_∞ controller such that the closed-loop system is stochastically stable and the cost function value is minimized. A numerical example is given to verify the effectiveness of this method.