A Neural Network System Stability Analysis And State Estimation

The studies of the Artificial Neural Networks (ANNs) consist of two aspects briefly: the studies of the theory and the studies of the application. The studies of theory include two classes. One is to develop new models which have more functions and better performance than those of the previous using mathematical methods and the based theories of neural networks. To develop better network algorithms and to research the performance of the new neural networks models such as stability, convergence, fault tolerance, robustness and so on; Another is to develop new network mathematical theory based on the achievements that have been made. For example, neural network dynamics, nonlinear neural field and so forth. The studies of the application may also include two classes. First, the research of the simulation of the software and the hardware realize of neural network; Second, the research of the application in other domains such as pattern recognition, signal processing, expert system, optimum composition, robot control, etc. The studies about the theory of the neural networks have significant meaning. The applications of neural network will be more thorough and more widely along with the development of the neural network theory itself as well as the correlation theories and the techniques.In this paper, we consider the asymptotical stability and state estimation problem of a class of delayed cellular neural networks(DCNNs) on the basis of the previous work. The main results can be listed as follows:In the first part, the problem of globally asymptotically stable for a class of cellular neural networks(CNNs) with constant time delay is considered. The problem we addressed is to apply the Lyapunov-Krasovskii functional theorem and some inequality technique, sufficient conditions are established to ensure the stability of the DCNNs, which are expressed in the form of linear matrix inequalities (LMIs). Numerical example is given to demonstrate the validity of the approach.In the second part, we deal with the globally asymptotically stability and robust stability problem for a class of time-varying delayed cellular neural networks, The problem we addressed is to apply the Lyapunov-Krasovskii functional theorem, sufficient conditions are established to ensure the stability of the DCNNs, which are expressed in the form of linear matrix inequalities (LMIs). Numerical example is given to demonstrate the validity of the approach. In the third part, the state estimation problem for a class of neural networks with time-varying delays is concerned. We constructed a new Lyapunov functional, which depends on the lower and upper bounds of the time-varying delay. Delay-dependent conditions are established in terms of LMI. A numerical example with simulation results is provided to demonstrate the effectiveness of the proposed design method.