Exponential Stability Analysis Of BAM Neural Networks With Time-varying Delays

This paper introduces neural networks, and we discuss the stability of the neural network systems. We make research on some ordinary neural network systems, and we analyze the difference and the stability of the systems. Since the neural networks was bron, many neural network models have been put forward. Every neural network model has its inherent advantages. Hopfield neural network system and Cohen-Grossberg neural neural network system are popular and widely applied in many fields.The neural network system is developing in direction of associative memory. These neural network systems with associative memory such as Hopfield neural network system, BAM neural network system and Boltzmann Machine have extensive prospect.Lyapunov function is a practical method about the neural network system, and is widely used to solve the problem of stability. Lyapunov theorem is a tool which can handle the problem of stability and asymptotical stability. We can construct a Lyapunov function, then we take the derivation of the function to make research on the properties of the system.BAM neural network is a hetero associative memory neural network, a recurrent neural network,and a double-layer neural network. It is put forward by Krosko in the 1980s. It is divided into two layers, and every layer is either input layer or output layer. The two layers are symmetrical, and the output layer will always send back message into the input layer until the system reach stable. The weight matrix of the BAM neural network is fixed and can not vary with the number of the iterations. BAM neural network has extensive use, and the main applications is pattern recognition, control systems, etc..The paper focuses on the neural network system with time-varying delays. We use the LMI method (linear matrix inequalities) to make research on it. LMI is a effective way to make research on the neural network system, and it combines the theory of matrices with the theory of ordinary differential equations. The LMI method uses known matrices to solve the unknown matrices by the LMI toolbox of matlab, and it can prove the right of the stability of the neural network system. This paper makes research on the two dimensional and one dimensional BAM neural network, and then we propose a sufficient condition. On this basis, we improve the condition,and the condition to be improved is less conservative.In a word, the focus of this paper is as follows, we construct a Lyapunov function, use the theory of LMI,and make research on the exponential stability of the BAM neural network system.