Stability Analysis Of Time-delay Systems Based On Linear Matrix Inequality

In control theory,the past state of the system will affect the current state to a certain extent.In other words,the change of the system is not only related to the current state,but also related to the past state.It is called a time-delay system.The time lag phenomenon may even cause system instability,so time lag has always been a research hotspot in the field of control.This paper uses Lyapunov's stability theory and functional differential equation theory,combined with the method of linear matrix inequality,to study two kinds of time-varying delay neural network stability problems.First,a class of global stochastic synchronization problems of neutral chaotic neural networks with Markov jump parameters under the mean square impulse is studied.With the help of drive response concept and time-delay feedback control technology,through the Lyapunov function method,vector Wirtinger-type inequality,novel inverse convex lemma and free weight matrix method,a sufficient condition is obtained to ensure that two identical Asymptotic synchronization of Markov jump chaotic delay neural network.The proposed results do not require the differentiability and monotonicity of the activation function,and then are checked by MATLAB.Finally,a numerical example with simulation is provided to illustrate the effectiveness of the proposed synchronization scheme.Then,the stability analysis of a gene regulatory network with time-varying delay is studied.This chapter uses differential equations to assess the stability of gene regulatory networks.The stability analysis is based on the Lyapunov method and the integral inequality method.The results expressed in the form of linear matrix inequalities can be easily verified by convex optimization techniques or software packages(MATLAB LMI Toolbox).The free weighting matrices used in deriving the existing stability standards make them less mathematically complex and computationally effective.