LMI Stability Criteria Research For A Class Of Neural Networks

The research on neural network can be tracked back to the end of19th century and the beginning of20th century. It is a new interdisciplinary developed form psychology, neurophysiology and physics.The birth of neural network has made a tremendous impact on electronic science, information science, mathematical science and other related fields. After more than half century tortuous development, it has become the most rapid development discipline and international frontier. At the same time, it has evolved into various forms of mathematic models and research branchs.Now, neural network has been widely applied to many other areas, such as image processing, automatic control,pattern recognition, signal processing, economic,chemical,and power system and so on.As is well known, in application process, most of neural network models are required to be stable ones. However, in the hardware implementation, the stability property always be interfered.Among all of these instable factors, time delay is one of the main reasons.Since the finite transmission speed time delay is inevitable, it has become a basic characteristic of the network. And it has impacts the dynamic behavior of network seriously. Time delay can lead to instability, periodic oscillations and even chaotic phenomenon. Thus, in the mathematical model of neural network, time delay should be considered. And the stability analysis for delayed neural networks is necessary, not only for the need of hardware realization, but also for the need of practical application.As the importance of delayed neural networks, this dissertation deeply analysised a class of special neural network model with time delays, and established the following results:(1) Combined with integral Jensen inequality, double integral Jensen inequality, reciprocal convex inequality, linear matrix inequalities (LMI) technology, and inequality technique, by constructing new Lyapunov functional, some new stability criteria are established. Additional, by deriving some new integral inequalities, some less conservative stable criteria are established further.(2) Considering the feature of neural network’s sector bounded constraint, by using convex theory, this dissertation transforms the nonlinear neural activation function into a linear express with parameter uncertainty. Combined with Finsler Lemma, delay decomposition technique, and piecewise convex Lyapunov function construction technique, some less conservative stable criteria are established further.(3) In order to illustrate the validity and superiority of the criteria established in this dissertation, some numerical examples are proposed.At last, by summarizing the major contributions of this work, we analyzed the advantages and disadvantages of the stability criteria established in this dissertation, and pointed out the direction and focus of future work.