Abstract
This paper addresses the problem of global fixed-time synchronization of two fractional chaotic systems with different dimensions in the presence of matched bounded and differentiable exogenous disturbances and uncertainties in the systems. Firstly, a novel fixed-time stable dynamical system is investigated wherein the upper bound estimate of the settling time of synchronization is determined by a priori value dependent on a design parameter regardless of the initial conditions. The introduced dynamical system to guarantee fixed-time stability is completely different from that in the existing works of literature. Based on the introduced fixed-time dynamic, a novel controller is designed that guarantees globally synchronization of two fractional chaotic systems with different dimensions within the fixed-time. Afterward, the result of synchronization of two different dimensional fractional chaotic systems within the fixed-time is extended to the networked ones. Finally, the effectiveness and validity of the results of the theoretical analysis are demonstrated by the illustrative examples and their numerical simulations.
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