International Journal of the Physical Sciences Vol. 7(2), pp. 273 - 280, 9 January, 2012 Available online at http://www.academicjournals.org/IJPS DOI: 10.5897/IJPS11.729 ISSN 1992 - 1950 ©2012 Academic Journals Full Length Research Paper Anti-synchronization of chaotic neural networks with time-varying delays via linear matrix inequality (LMI) Yousef Farid*, Nooshin Bigdeli and Karim Afshar Department of Electrical Engineering (EE), Imam Khomeini International University, Qazvin, Iran. Accepted 28 December, 2011 In this paper, anti-synchronization problem of two identical chaotic neural networks with time-varying delays is proposed. By using time-delay feedback control technique, mean value theorem and the Leibniz-Newton formula, and by constructing appropriately Lyapunov-Krasovskii functional, sufficient condition is proposed to guarantee the asymptotically anti-synchronization of two identical chaotic neural networks. This condition, which is expressed in terms of linear matrix inequality, rely on the connection matrix in the drive and response networks as well as the suitable designed feedback gains in the response network. Finally, the anti-synchronization of two chaotic cellular neural network and Hopfield neural network with time-varying delays are considered to illustrate the effectiveness of the proposed control scheme, in which, when compared with the nonlinear feedback control method, the proposed method shows superior performance. Key words: Lyapunov-Krasovskii functional, chaotic neural networks, anti-synchronization, time-varying delay, linear matrix inequality. INTRODUCTION Over the recent decades, existence of chaos has been discovered and reported in different aspects of science and technology, such as electrical circuits, chemical reactions, information processing, lasers, optics and neural networks (Chen and Dong, 1998; Wieczorek and Chow, 2009; Yang and Yuan, 2005; Gutzwiller, 1990). Since Pecora and Carroll (1990) established a chaos synchronization scheme for two identical chaotic systems with different initial conditions, chaos synchronization has attracted a great deal of attention (Sun and Cao, 2007; Sanjaya et al., 2010). Another interesting phenomenon discovered was the anti-synchronization (AS), which is noticeable in periodic oscillators. AS is a phenomenon that the state vectors of the synchronized systems have the same amplitude but opposite signs as those of the driving system. In this case, the sum of two signals is expected to converge to zero. So far, different techniques and methods have been proposed to achieve chaos anti- synchronization, such as, active control method (Ho et *Corresponding author. E-mail: yousef.farid @ikiu.ac.ir. Tel: +98 281 8371164. Fax: +98 281 3787777. al., 2002), adaptive control (Li et al., 2009), H ∞ control (Ahn, 2009), nonlinear control (Al Sawalha and Noorani, 2009), sliding mode control (Chiang et al., 2008), backstepping control (Hu et al., 2005), adaptive modified function projective method (Adeli et al., 2011), etc. Recently, the study of dynamical properties of neural networks appears more due to their extensive applications in differential fields, such as signal and image processing, pattern recognition, combinatorial optimization and other areas (Cohen and Grossberg, 1983; Carpenter and Grossberg, 1987; Chua and Yang, 1988). In the electronic implementation of the neural networks, time delay will occur in the interactions between the neurons inevitably, and will affect the dynamic behavior of the neural network models and may lead to instability and/or deteriorate the performance of the underlying neural networks. In some particular cases, it has been shown that these networks can exhibit some complicated dynamics and even chaotic behaviors if the network’s parameters are appropriately chosen (Yuan, 2007; Lu, 2002). An efficient tool for solving many optimization problems is linear matrix inequality approach which has been