Research On The Stability And Passivity Of Time-varying Time-delay Neural Networks

In recent decades,in the field of control,nonlinearity and time delay have been the focus and hotspot of neural network systems.In the specific realization and professional application of the neural network system,the fixed transmission time of the neuron and the limited information transmission rate will inevitably lead to the system delay.In addition,environmental noise,unknown parameters,and interference often encountered in various actual projects.This makes it very difficult to develop accurate mathematical models.The existence of uncertainty inevitably degrades system performance and even makes dynamic systems unstable.Nowadays,combined with complex unknown nonlinear system problems,the rolling optimization control can better adapt to the actual system and have stronger robustness.However,few scholars have studied adding random parameter uncertain factors to rolling optimization control.In addition,the theory of system stability can be analyzed from the passivity,which is a comprehensive analysis method of passivity.Therefore,it is necessary to study the passive problem of neural networks with leakage delay.When combining theory and actual conditions with neural network modeling,adding parameter uncertainties is also a crucial and inevitable consideration.Therefore,to address the above-mentioned problems,the first study is the stability analysis of the rolling optimization of neural networks with time-varying delays in this paper.On the one hand,construct a complex Lyapunov-Krasovskii functional(LKF)with more useful information.On the other hand,this article uses a more general and stricter integral inequality method based on auxiliary functions than some existing integral inequalities,and deals with the new cross-term matrix of the matrix.Therefore,some new matrix variables containing more information are generated,giving the result more degrees of freedom.In addition,a new condition for optimizing the final weighting matrix of the cost function is obtained,thereby reducing its conservativeness and increasing its upper limit of delay.Finally,the simulation value is compared with the previous article to illustrate the superiority of this method.Secondly,this paper also studies the robustness and passivity of neural networks with leakage delays.By selecting the appropriate LKF,using Wirtinger's inequality and free weight matrix methods to improve the delay standard,and expressing it in the form of linear matrix inequality,the generalized activation function is realized.Sufficient conditions are established to ensure the robust stability and passivity of the neural network under consideration.Finally,using the LMI toolbox to give the system state trajectory diagram can be seen,which proves the validity and conservativeness of the standard proposed in this paper.Finally,the neural network combined with the above research adds a random parameter uncertainty(ROU)factor.The ROU follows some uncorrelated Bernoulli distribution white noise sequences,which can enter the neural network in a free and random manner.Using a suitable lemma,the ROU problem added in this article is transformed into a linear matrix inequality.The rolling optimization analysis of neural networks with random uncertainties provides a new time-delay related condition to ensure a less conservative delay-dependent stochastic stability criterion.It can be seen from the experiments given that the validity of the standard proposed in this paper is proved.