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Top1. Introduction
Dynamic systems with chaotic behavior are complex nonlinear systems with that widely appear in both nature and man-made systems. However, in some practical situations, this chaotic behavior is not desirable and needed to be controlled. On the other hand, this behavior founds a wide number of applications and mostly those applications can be achieved by synchronizing two chaotic systems. Due to the complex nonlinear dynamic behavior of chaotic systems, the problems of chaos control and synchronization is always difficult and challenging.
Synchronization of chaotic systems has received a significant attention and plays an important role in nonlinear science during the last two decades (Pecora, 1990; Agiza, 2004; Nayfeh, 1995; Takeo, 2005; Yau & Sheih, 2008). Recently, chaos and its synchronization have found several useful applications in many fields of engineering and science, such as in secure communication, biological systems, power converters, chemical reactions, and information systems, etc. (Chen & Dong, 1998). Many approaches have been presented for synchronization of chaotic systems such as periodic parametric perturbation method (Astakhov et al., 1997), drive-response synchronization method (Yang et al., 1999), adaptive control method (Wang et al., 2004; Chua et al., 1996; Liao, 1996; Lian et al., 2002; Wu et al., 1996), variable structure (sliding mode) control method (Fang et al., 1999; Yau, 2004), and backstepping control method (Wang & Ge, 2001; Bowong & Kakmeni, 2004; Lu & Zhang, 2004).
Since introduced by Zadeh (1965), fuzzy systems have received more attention and have been successfully adopted in a wide variety of engineering disciplines including control systems and signal processing applications (Wang, 1994). The key features of fuzzy logic systems behind its great success are that it can incorporate linguistic information from human experts and provides effective and systematic framework to handle nonlinear systems especially complex and ill-defined systems. Several fuzzy-based schemes are used for chaos synchronization and control. In Yau and Sheih (2008), classical fuzzy logic is used to design a robust controller, where the fuzzy rules are subject to a common Lyapunov function such that the error dynamics satisfies stability in Lyapunov sense. Also, many T-S fuzzy based-observer and controller methods which are based on parallel distributed compensation (PDC) are found in Tanaka et al. (1998), Kim et al. (2005), Ting (2005), and Hayon et al. (2006). However, satisfactory results are obtained; these approaches are based on the assumption that the system dynamics must be known.