Some New Criteria For Synchronization Of The Master-Slave Chaotic Lur 'e Systems

Chaos synchronization is one of the hottest topics in the field of nonlinear science,and has many applications to a wide range of fields,including physics,biomedical engineering,and secret communications,etc.This dissertation investigates the new algebraic criteria for the synchronization of two classes of chaotic systems,Chua's circuits and the multi-scroll chaotic Jerk systems,under linear state error feedback control.The main works can be summarized as below.The first part of work studies lag synchronization of the master-slave chaotic Chua's circuits via linear state-error feedback control with channel delay base on the Lyapunov stability theorem.Several algebraic criteria for the chaotic lag synchronization subject to the special control gain matrices are rigorously proven by means of the Strum's theorem and the factorization theorem in polynomial theory.The numerical examples verify the novel criteria are less conservative by comparing with the existing such criteria.The second part of work deals with the synchronization of the master-slave multi-scroll chaotic Jerk systems via the linear state-error feedback control.A frequency domain criterion for chaos synchronization subject to the general control matrix and the algebraic criteria for chaos synchronization subject to the special and simple control matrices are rigorously proven by means of the absolute stability theory.The Sturm's Theorem is then utilized to derive an optimized synchronization criterion.The numerical examples verify the effectiveness of the new criteria.