Types Of Neural Networks With Delay Stability Study

In resent years, the dynamical issues of delayed neural networks have attracted worldwide attention. A lot of interesting stability criteria for the equilibrium solutions of delayed neural networks has been obtained, such as the global asymptotic stability, robust stability, global exponential stability etc. In this paper, the stabilities of neural networks with discrete and distributed time-varying delays, fuzzy neural networks with discrete and distributed time-varying delays and BAM neural networks of neutral-type with time-varying delays are studied. It is divided into five parts.1. Firstly, the background and evolution of stability of neural networks are proposed.2. The Lyapunov Stability Theories and the Linear Matrix Inequalities (LMI) method included some useful lemmas which are needed in our research are introduced.3. The stability of neural networks with discrete and distributed time-varying delays is discussed. Firstly, we construct the appropriate Lyapunov-Krasovskii functional, and then add some appropriate zero terms to the deviation of the Lyapunov functional and use Linear Matrix Inequality (LMI) technique to construct some linear matrix inequalities. Some delay-dependent sufficient conditions have been obtained for global robust asymptotic stability of such systems. A numerical example is given to demonstrate the effectiveness of our results.4. The stability of fuzzy neural networks with discrete and distributed time-varying delays is discussed. Based on the character of the system itself and using T-S model, by constructing an appropriate Lyapunov-Krasovskii functional and using Linear Matrix Inequality (LMI) technique and Leibniz-Newton formula, the state feedback controller of the fuzzy neural networks has been designed and some sufficient conditions have been gained for the solvability of the problems of robust stabilization and robustly stable with an H∞performance level for a class of uncertain T-S fuzzy neural networks with both discrete and distributed time delays.5. The stability of BAM neural networks of neutral-type with control input is discussed. Based on the neutral-type of the system, by constructing a stable operator which is usually used to discuss the neutral differential equations and by using appropriate Lyapunov functional as well as Razumikhin's method and norm inequalities, several sufficient delay dependent conditions have been derived under the given state feedback controller for checking the global asymptotical stability and global exponential stability of BAM neural networks of neutral-type with time-varying delays and control input.