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The problem of robust guaranteed cost control for a class of uncertain stochastic systems with Markov jump parameters subject to actuator saturation is discussed. 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 guaranteed cost 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 guaranteed cost 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.