Stability Analysis Of Delayed Neural Networks Based On Integral Inequality

The time delay of the system is inevitable in the practical applications,and the delay is a major factor leading to the instability of the systems.In recent years,the method of constructing suitable Lyapunov-Krasovskii functional(LKF)and using integral inequality to deal derivatives of the functional has been widely used in the stability and relevant analysis of time-delay systems.In this study,several kinds of common neural networks are used as the research object.By constructing a augmented Lyapunov functional and using the new auxiliary function-based and more general integral inequality,a less conservative delay-dependent stability and relevant criteria is established.And based on MATLAB linear matrix inequality(LMI)toolbox,several numerical examples demonstrate the effectiveness of the theorem.The main work is as follows:1.The problem of delay dependent stability of time-delay cellular neural networks(CNN)has been investigated.According the characteristics of time-delay cellular neural network model,construct a suitable Lyapunov functional.Then by using Jensen inequality,new integral inequality and other relevant lemmas to estimate the derivative of the functional,a delay dependent stability criteria can be derived.On this foundation,by relaxed the criteria's condition,a new and less conservative stability theorem can be deduced.Finally,three numerical examples are given to verify the validity of the theorems.2.The stability theorem of generalized time-varying delayed neural networks has been proposed.Firstly,considering the influence among more variables,an augmented LKF is constructed.By expanding the new integral inequality,use some different lemmas from cellular delayed neural network stability analysis to deal the derivative of the augmented functional.At last,a less conservative delay dependent stability criteria of generalized delayed neural network is obtained by numerical simulation.3.The problem of passivity analysis for neural networks with discrete and distributed delays is considered.It's better to analysis system's stability by establishing connections between the passivity theory and Lyapunov stability theory.So to analysis the delayed system's passivity by utilizing the new inequality.A suitable Lyapunov-Krasovskii candidate is constructed and using the simplest form of the new inequality and other related lemmas to handle the derivative of the functionals.In terms of the definition of passivity and by introducing the input and output vectors,the system's passivity criteria is deduced.According to some transformation,the uncertain system with discrete and distributed delays is obtained and through the same method,the robust passivity theorem is derived.Finally,numerical examples are given to prove that the new theorem can effectively improve the upper bound of the system delay.