The Research On The Stability Of Neural Networks With Interval Time-varying Delays

In this paper, in order to study the stability of neural networks with interval time-varying delays, the stability and related theories of functional differential, and combined with the linear matrix inequality techniques, which getting a new condition for stability of the zero solution of neural network system.Firstly, the study of neural networks with time-varying delays. The rule of h₁≤h（t）≤（h₁+h₂）/2and（h₁+h₂）2≤h（t）≤h₂ is applied into the interval division of time delay to reduce the conservatism of the obtained results. The paper shows the conditions for the asymptotic stability of system on each time delay, which mixes with double integral by constructing an appropriate LKF. To deal with the derivative of V function, the free weight matrix, Jessen inequality, the inverse convex inequality and free-weighting matrices and other techniques have been used. In the end,numerical simulation and analysis are given to illustrate the superiority of our theorem.Secondly, we deal with the robust stability problem for neural networks with interval time-varying delays and parameter uncertainties by choosing an appropriate Lyapunov function.Some stability criteria are derived based on the LMI.But this criteria with the perturbation function C（t）, In order to obtain a criteria without perturbation function C（t）, we give another stability criteria.This paper also gives the conditions for the stability of the system with no activation function, which is the last corollary. All the conclusion through the experiment to prove its feasibility and correctness.Finally, the study of the stability of time-varying delay systems with disturbances.The stability criteria are derived based on choosing an appropriate Lyapunov function,this criteria with the perturbation function. Then, we transform the conditional to new condition by using some technology of LMI. The paper also offers the conditions for the stability of the system with no disturbance---corollary 1. At the end of the paper,the numerical simulation and analysis are given to illustrate the superiority and correctness of our theorem.