This paper proposes the generalized projective synchronization for chaotic heavy symmetric gyroscope systems versus external\r\ndisturbances via sliding rule-based fuzzy control. Because of the nonlinear terms of the gyroscope, the system exhibits complex\r\nand chaotic motions. Based on Lyapunov stability theory and fuzzy rules, the nonlinear controller and some generic sufficient\r\nconditions for global asymptotic synchronization are attained. The fuzzy rules are directly constructed subject to a common\r\nLyapunov function such that the error dynamics of two identical chaotic motions of symmetric gyros satisfy stability in the\r\nLyapunov sense. The proposed method allows us to arbitrarily adjust the desired scaling by controlling the slave system. It is\r\nnot necessary to calculate the Lyapunov exponents and the Eigen values of the Jacobian matrix. It is a systematic procedure\r\nfor synchronization of chaotic systems. It can be applied to a variety of chaotic systems no matter whether it contains external\r\nexcitation or not. It needs only one controller to realize synchronization no matter how much dimensions the chaotic system\r\ncontains, and the controller is easy to be implemented. The designed controller is robust versus model uncertainty and external\r\ndisturbances. Numerical simulation results demonstrate the validity and feasibility of the proposed method.
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