Abstract
This paper presents a discrete-time sliding mode control scheme for a class of master–slave (or drive-response) chaotic synchronization systems. The proposed scheme guarantees the stability of closed-loop system and achieves the global synchronization between the master and slave systems. The structure of slave system is simple and needs not be identical to the master system. Moreover, the selection of switching surface and the existence of sliding mode have been addressed. Numerical simulations are given to validate the proposed synchronization approach.
1. Introduction
Chaotic behavior is an interesting phenomenon appearing nonlinear systems and has been received more and more attentions in the last decades. A chaotic system is a highly complex dynamic nonlinear system. The prominent characteristic of a chaotic system is its extreme sensitivity to initial conditions and the system’s parameters, and this makes the problem of chaotic synchronization much more important. In the last few years, chaotic synchronization has applied in vast area of physics and engineering systems such as in chemical reactions, power converter, biological systems, information processing, especially in secure communication [1–3]. Many methods have been developed to realize the problem of the synchronization of chaotic systems including state feedback method [1,2,4–10], the observer method [3,11–15] and output feedback method [16]. However, these methods are developed in continuous-time system. To the best of the author’s knowledge, the problem of synchronizing uncertain chaotic systems in discrete-time domain has not been fully investigated and is still open in the literature. This has motivated our research.
5. Conclusions
In this paper, a discrete-time SMC scheme has been proposed for synchronization of a class of chaotic systems. It has been shown that the proposed control scheme ensures the stability of synchronization error dynamics, and provides good chaotic synchronization between the master and slave systems. The control design is rather straightforward and easy to implement for chaotic synchronization. The discrete-time SMC needs not a switching type of control law. Chattering phenomenon and reaching phase are eliminated. Moreover, the control strategy can be easily applied to other dimensional chaotic synchronization problems. Numerical simulation has confirmed the validity of the proposed synchronization scheme.
