Passivity based sliding mode control and synchronization of a perturbed uncertain unified chaotic system

The problem of passivity-based sliding mode control is considered, for the unified chaotic system having uncertainties and perturbations. Using a combination between sliding mode method and the passivity method, an appropriate switching surface for the uncertain and perturbed system is designed, and then through passivity theory, the stability of the system is ensured. The proposed design is applied in two control problems, the first one being the stabilization of the uncertain perturbed unified chaotic system and the second one is the synchronization between two unified chaotic systems, where only the slave system contains uncertainties and perturbations. Finally, the effectiveness of the proposed methods are illustrated through numerical simulations, and also through a microcontroller implementation. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.