Robust finite-time composite nonlinear feedback control for synchronization of uncertain chaotic systems with nonlinearity and time-delay

This paper proposes a combination of finite-time robust-tracking theory and composite nonlinear feedback approach for the finite-time and high performance synchronization of the chaotic systems in the presence of the external disturbances, parametric uncertainties, Lipschitz nonlinearities and time delays. The composite nonlinear feedback control technique develops an accurate and high-performance response for the following of the master chaotic system and the finite time concept provides the convergence of the error signals to zero in the finite time. Therefore, in this work, we will develop a new finite time robust tracking and model following control approach based on the composite nonlinear feedback scheme. Using the Lyapunov stability approach, we have proved that the tracking errors of the uncertain chaotic system converge to the origin in the finite time. Moreover, a sufficient criterion is derived to guarantee the robust asymptotic stability of the synchronization error dynamics. Simulation results on Chua's chaotic system are presented to prove the performance of the suggested controller compared to the other technique.