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The paper deals with a switching performance optimal control for continuous-time controller switched systems. Steady-state bumpless switching is considered. An linear matrix inequality (LMI) based static bumpless switching compensator design is given via internal model principle, guaranteed cost and regional pole placement technique. The corresponding bumpless switching scheme is also presented. The proposed scheme is simple in structure, and easy to be implemented. Simulations for the generic hypersonic vehicle model show the effectiveness of the proposed method.