Abstract By constructing two scaling matrices, i.e., a function matrix Λ ( t ) $Lambda (t)$ and a constant matrix W which is not equal to the identity matrix, a kind of W − Λ ( t ) $W-Lambda(t)$ synchronization between fractional-order and integer-order chaotic (hyper-chaotic) systems with different dimensions is investigated in this paper. Based on the fractional-order Lyapunov direct method, a controller is designed to drive the synchronization error convergence to zero asymptotically. Finally, four numerical examples are presented to illustrate the effectiveness of the proposed method.
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