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This paper addresses the global anti-synchronization of chaotic parametrically excited pendulums under linear feedback control. Based on the master-slave anti-synchronization scheme with linear feedback control, a sufficient algebraic criterion for the global anti-synchronization of two parametrically excited pendulums are proved by means of Lyapunov stability theorem and further improved by the optimization technique. Then some simpler anti-synchronization criteria are obtained. Finally, the effectiveness of the obtained criteria is verified by a numerical example.