Design of a sliding mode controller for synchronizing chaotic systems with parameter and model uncertainties and external disturbances

Abstract

Finite-time synchronization of two different uncertain chaotic systems using a new non-singular terminal sliding mode approach is studied in this paper. Both master and slave systems are perturbed by parameter and model uncertainties, as well as external disturbances. A novel non-singular terminal sliding manifold is introduced. Based on the Lyapunov stability theory and finite-time control idea, a robust sliding mode controller is designed. It is shown that both reaching and sliding phases have the finite-time convergence property. In other words, it is proved that the state trajectories of the slave system can reach the state trajectories of the master system in a given finite time. The robustness and applicability of the proposed technique are demonstrated by two illustrative examples.