Design of hybrid controller for synchronization control of Chen chaotic system

Volume 10, Issue 6, pp 3320--3327 http://dx.doi.org/10.22436/jnsa.010.06.41

Publication Date: June 25, 2017 Submission Date: January 02, 2017

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Authors

Xiaoyu Zhang - School of Mathematics and Statistics, Shandong Normal University, Ji’nan, 250014, P. R. China. Xiaodi Li - School of Mathematics and Statistics, Shandong Normal University, Ji’nan, 250014, P. R. China. - Institute of Data Science and Technology, Shandong Normal University, Ji’nan, 250014, P. R. China. Xiuping Han - School of Mathematics and Statistics, Shandong Normal University, Ji’nan, 250014, P. R. China.

Abstract

This paper deals with the synchronization control of Chen chaotic system using a hybrid control which includes continuous state feedback control, the impulsive control and the nonlinear feedback law. To this end, a hybrid controller based on linear matrix inequality (LMI) and average dwell time (ADT) is derived by employing impulsive control theory. The main advantage of the result lies in that, for one thing, they are complementary to each other, that is, when the impulse inputs occur in terms of disturbances which do harm to the synchronization, the continuous state feedback control will cover the weakness and stabilize the error system, and conversely, when the continuous state feedback control is given in terms of external disturbances which do harm to the synchronization, the impulsive control input will stabilize the error system; for another, the developed result is based on ADT condition and dropped the restriction on the upper and lower bounds of the impulsive intervals. Finally, numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.

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Keywords

• Chen system
• impulsive control
• synchronization
• average dwell-time (ADT)
• hybrid controller.

MSC

•  34K35
•  34D06
•  34K34

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