Abstract: The robust H_∞ control problem for impulsive Markov switching linear stochastic systems with external distur-bance is considered.The systems' robust stability and robust capability are analyzed respectively.Firstly,multiple Lyapunov method is used to analyze the stability of the systems,and the sufficient conditions are derived for the robust stability in probability of the system.Furthermore,by analyzing the robust capability of the system using the linear matrix inequality(LMI) method,the state feedback gain matrix and the impulsive control gain matrix of the system are obtained,and then a robust H_∞ control rule is derived.Finally,a robust H_∞ control design based on MATLAB is presented,and a numerical example shows the effectiveness of the proposed approach.