A New Robust Stability Criterion For Dynamical Neural Networks With Mixed Time Delays

As a multi-disciplinary research area combining information science, neural psychology and brain science, artificial neural network is a current hi-tech research hotspot. It is of great theoretical and practical significance to do research on the dynamic system of neural network, find out the features of neural network dynamic system, and deal with factual problems in the field of engineering technology with the help of neural network theory, for the neural network dynamic behavior is an important part of neural network theory.In the study of neural dynamic system, the stability theories of the differential equation and functional differential equation are important tools to study neural network dynamic system, especially for the research on the variation tendency of the solution to the neural network system. Therefore, we construct Lyapunov-Krasovskii functional with the aid of the relevant theories of inequality analysis techniques and matrix analysis to study the stability related problems of neural network system. At the same time, the stability criteria of the solutions to the neural network system are put forward in the form of linear matrix inequality, with the help of ancillary matrix calculated by using mathematics software package. In addition, the techniques of magnifying and shrinking inequation and relative lemmas are flexibly applied in the research of neural network stability related problems to reduce the conservatism of the system.Based on existing theories and research results, this dissertation adds the distributed delay to neural network system, for in reality, the past has a great influence on the present, and not only can some specific moments in the past influence the present.Accordingly, the distributed delay is added to the system on the basis of discrete delay.Three different methods of magnifying and shrinking inequation are employed to do research on the existence, uniqueness and globally asymptotic stability of the uncertain balance point of mixing time delay and parameter. To start with, the principle of homeomorphism mapping is applied, and then the upper bound of incidence matrix of neural network is introduced, and then the sufficient conditions of the existence of balance point of several neural network systems are given. Hence, under these circumstances, with appropriate application of Lyapunov-Krasovskii functional, we have proved that the neural network system for the robust stability of equilibrium isglobal. Numerical experiments show that the stability conditions we obtained by neural network system is feasible and the conservatism of the stability conditions of the neural network system is reduced.