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

In the recurrent years, neural networks have been studied extensively and have been widely applied within a kind of engineering fields, such as energy transfer, image recognition, optimization calculation signal processing and artificial network. Neural network also have been extensively paid attention by mathematics, computer, automatic control, and other areas of the discipline of scholars.in order to better understand the dynamic behavior of different network, we need to have a stable system, which makes the stability Analysis of the neural network model analysis become necessary. In the study of neural dynamic system, the stability theories of the differential equation and functional differential equation are important tools in studying neural network dynamic system, especially for the research on the variation tendency of the solution to the neural network system.This paper mainly study the problem of stability analysis for delayed recurrent neural networks, and the research achievements are mainly shown in the next part.First of all, this paper investigated the problem of stability analysis of static recurrent neural networks with additive time-varying delay. By constructing the Lyapunov functional and applying the LMI formula tighter upper bound of the derivative of the Lyapunov functional, new stability criterion is derived.Secondly, this paper investigated the problem of stability analysis of neural networks with discrete and distributed time-varying delay. By constructing a suitable Lyapunov functional and applying the LMI formula, zero-equalities, reciprocally convex approach tighter upper bound of the derivative of the Lyapunov functional, new stability criterion is derived. Finally, numerical example are provided to demonstrate the effectiveness of result.In this paper, one improved global exponential stability criterion for recurrent neural networks with time-varying delay is proposed. A suitable Lyapunov functional has been proposed to derive some less conservative delay-dependent stability criteria by using the free-weighting matrices method and the convex combination theorem.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.The result has better applicability. There has certaintheoretical significance and use value for the recurrent neural network.