This paper considers the finite-time synchronization of chaotic systems in the presence of model uncertainties and/or external disturbances. The synchronization happens between the two nonlinear master and slave systems. Control law is designed in such a way that the state variables of the slave system follow the state variables of the master system in the presence of uncertainties and external disturbances. In order to design a robust finite-time controller, first, a novel terminal sliding surface is proposed and its finite-time convergence to zero is analytically proved. Then a terminal sliding mode controller is designed which can conquer the uncertainties and guarantees the finitetime stability of the sliding motion equations. In this regard, a theorem is proposed and according to the Lyapunov approach it is proved that the synchronization happenes in finite-time. Additionally, in order to show the applicability of the proposed controller, it is applied on two practical systems, the Duffing-Holmes system and chaotic gyroscope system. Computer simulations verify the theoretical results and also display the effective performance of the proposed controller.
ARTICLE HISTORY