Global finite-time lag synchronization for a class of chaotic systems with the cubic terms in the presence of time delay

摘要

This paper designs a simple, continuous and dimension-reducible controller, named the variable substitution and feedback controller, to deal with the global finite-time lag synchronization for a class of chaotic systems with cubic terms in the presence of time delay. Under the new designed controller, the finite-time lag synchronization scheme is built up after the description of a class of chaotic systems with cubic terms. Then the finite-time stability theory is applied to prove some criteria for the global finite-time lag synchronization of this class of chaotic systems and estimate the synchronization time by transforming the global finite-time lag synchronization problem to the global finite-time stability of the error system, which originates from the established finite-time lag synchronization scheme for this class of chaotic systems. Then, the obtained criteria are applied to the modified Chua's circuit system, further attaining a criterion on the global finite-time lag synchronization of the Chua's circuit systems. Finally, a numerical example is provided to verify the effectiveness of the newly obtained criterion.