Synchronization Criteria For The Master-slave Chaotic Systems Via Variable Substitution Control

Synchronization is one of the research hotspots in the field of non-linear science and system control.Chaotic synchronization problem exists widely in biomedical engineering,secure communication,electronic information and other fields.It has scientific value and practical application prospects.In this paper,the problem of global chaotic synchronization of generalized Lorenz chaotic system and Jerk chaotic system via variable substitution control are investigated.The main works can be summarized as below.(1)Chaos synchronization of the master-slave generalized Lorenz systems via variable substitution control is investigated.A few of criteria for both the global chaos synchronization and the non-synchronization of the master-slave generalized Lorenz systems under a single-variable substitution control are rigorously proven.These criteria are then applied to analyze the master-slave synchronization for the classical Lorenz systems,Chen systems,Lü systems and the unified chaotic systems,obtaining the new conclusions.(2)Chaos synchronization of the master-slave Jerk systems via variable substitution control is investigated.Based on the theory of absolute stability,both a linear matrix inequality(LMI)criterion and the frequency domain criteria for the global synchronization of the master-slave Jerk systems are rigorously deduced.The simulation examples verify the effectiveness of the proposed criteria.