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H-infinity control is an important kind of robust control method, it with h-infinity norm as the control performance index, is a kind of optimal control method, purpose is to find the internal stability of controller, the infinite norm of the closed-loop transfer function, achieve the goal of control.With fixed high linear level inverted pendulum as control object, realize the Riccati equation and LMI algorithm based h-infinity controller design, the system is realized by using M documents and simulink modeling, controller design, validation of the complete system algorithm, the experimental results show that the output of the controller, the change of the state variables of inverted pendulum system was stable, the system has strong robustness, the system shows good dynamic quality and effectiveness of h-infinity controller is verified.