The adaptive sliding synchronization of uncertain Duffing-Holmes fractional-order chaotic systems with dead-zone

Abstract

This article investigates the problem of adaptive sliding synchronization for Duffing-Holmes fractional-order chaotic systems in the presence of dead-zone, disturbance, and uncertainty. It starts by estimating dead-zone parameters, and then adaptive laws are used to compensate the dead-zone parameters. In the second step, a sliding mode controller is designed so that the slave system can follow the master system. The fractional type of Lyapunov is implemented to prove stability. The proposed adaptive sliding mode controller guarantees the asymptotic stability of system despite the presence of the dead-zone and uncertainty. Simulation results show the validity and effectiveness of the proposed controller for synchronization of Duffing-Holmes fractional-order chaotic systems perturbed by the dead-zone, disturbance, and uncertainty.