A generalized finite-time analytical approach for the synchronization of chaotic and hyperchaotic systems

Purpose: The purpose of this paper is to develop some interesting results in the field of chaotic synchronization with a new finite-time controller to reduce the time of convergence. Design/methodology/approach: This article proposes a finite-time controller for the synchronization of hyper(chaotic) systems in a given time. The chaotic systems are perturbed by the model uncertainties and external disturbances. The designed controller achieves finite-time synchronization convergence to the steady-state error without oscillation and elimination of the nonlinear terms from the closed-loop system. The finite-time synchronization convergence reduces the hacking duration and recovers the embedded message in chaotic signals within a given preassigned limited time. The free oscillation convergence keeps the energy consumption low and alleviates failure chances of the actuator. The proposed finite-time controller is a combination of linear and nonlinear parts. The linear part keeps the stability of the closed-loop, the nonlinear part increases the rate of convergence to the origin. A generalized form of analytical stability proof is derived for the synchronization of chaotic and hyper-chaotic systems. The simulation results provide the validation of the accomplish synchronization for the Lu chaotic and hyper-chaotic systems. Findings: The designed controller not only reduces the time of convergence without oscillation of the trajectories which can run the system for a given time domain. Originality/value: This work is originally written by the author.