Stability Analysis For Three Types Of Neural Networks With Time-Varying Delay

The research of neural network can be traced back to the 18th century.Neural network is an intelligent control technology, it can simulate human intelligence behavior and solve the traditional automation technology that can not solve the many complex and uncertain nonlinear automation. At the same time,it is an interdisciplinary, involving biology, physiology, electronics, computer science, mathematics and physics and other disciplines, these disciplines interact and help each penetration and mutually reinforcing. Current neural network is in a large-scale and multi-domain applications, which involves the application of almost all areas of society.So,in recent decades, the study of neural networks attracted widespread attention in academic circles.Time-varying delay neural network theory and applied research is the one of the international forefront topics of the neural network. It is well known that the delay in electronic implementation of neural networks is inevitable. The existence of time-delay makes thar the system analysis and synthesis become more complex and difficult, while the existence of time-delay is the root of system unstable and the deterioration of system performance. On the other hand,time-varying delay is not only a reflection of the switching speed of amplifiers with limited hardware in artificial neural network, but also in order to better simulate biological neural network delay characteristics, at the same time it resolve certain practical problems.This paper includes five chapters. Chapter 1,chapter2 briefly introduces the development and the stability theory of neural network.In chapeter 3, we introduce the stability of the neural network with interval-like time-varying delay, by constructing Lyapunov functional, we get the stability criteria that has been described by linear matrix inequality. In the given stability criterion, we don't need the restriction that the derivative of discrete time-varying delay is less than one.In Chapter 4, we disscuss the exponential stability of the BAM neural network,by constructing appropriate Lyapunov functional, combined with linear matrix inequality techniques, we get the stability criterion of BAM neural network, The criteria can use Matlab's LMI Control Toolbox effectively solving, numerical examples show the stability criteria is more effectiveness.In Chapter 5, we discuss the global exponential stability of the stochastic neural network, by constructing a novel Lyapunov functional and appling of stochastic analysis techniques, we get the global exponential stability criterion, and taking into account the exponential stability convergence rate of system.