Delay-Dependent H_∞ State Estimation Of Neural Networks With Mixed Time-Varying Delays

In recent years, the theory and application of Neural network has been developed rapidly. It has been applied in variable research fields, especially in industrial sectors, clinical medicine, economic activity. And it also can establish pattern recognition of facing system, automatic pattern recognition system, etc. So it has important theoretical and application value to research the stability of the neural network system.This paper is aim to research the issue of Delay-dependent H∞ state estimation of neural network with mixed time-varying delays. To discuss three kinds of neural networks system by using function different equation and neural network theory, which can obtain the following research results.Firstly, we deal with the problem of the neural networks system with discrete time-varying delay. By constructing the appropriate Lyapunov-Krasovskii function and using the inequalities analysis skills, which can obtain the auxiliary Lyapunov-Krasovskii function is positive. And then to establishing the H∞ standard of the neural networks and we can get the effectiveness of the results by illustrating numerical examples.Secondly, we deal with the stability of neural networks system with mixed time-varying delays. Using the delay-partitioning methods constructing the appropriate Lyapunov-Krasovskii function in the proof. And then using the inequalities analysis skills, which can obtain the condition of the asymptotic stability of the solution of the system.Thirdly, we deal with the problem of delay-dependent H∞ state estimation of the neural network with mixed time-varying delays. According to the characteristic of the activated function, constructing the suitable Lyapunov-Krasovskii function. Under the condition of adding zero equations, estimating the criterion of the neural networks with mixed time-varying delays. And then we can get the effective conclusion by showing the numerical examples.