Stability Analysis For Some Classes Of Uncertain Neural Networks With Time-Delay

Neural network is not only a kind of complex large-scale nonlinear dynamical systems, but also the adaptive organization system, which has various dynamics properties. Over the past decades, neural network has been applied to associative memory, pattern recognition and optimization problems. With the rapid development of science and technology, neural network has became an intersectional branch of science, which is referred to biological, physics, mathematics, computer, electronic and other disciplines. Recently, the stability problem of neural network has been paid considerable attention by domestic and scholars. In addition, as a branch of neural network, gene regulatory network has attracted the considerable attention of scholars at home and abroad, and making it become a new research field of neural network. Therefore, the stability analysis for uncertain neural network with time-delay has theoretical and practical significance.In this paper, the problems of stability and passivity for uncertain neural network with time-delay and the gene regulatory network stability have been investigated. Firstly, by using Lyapunov-Krasovskii functional method, related lemmas(such as the Shcur complement lemma, etc.), free weighting matrix and delta operator method, some new criterions for stability analysis of neural network can be expressed in terms of linear matrix inequalities(LMIs). Secondly, we have studied the problem of stability analysis for the genetic regulatory network, and by using the delta operator method and free weighting matrix, the corresponding conclusions can be obtained. Finally, we have summarized the research work, and pointed out the future work.