Research On Mean-Square Exponential Stability And Robust H_? Control Of Uncertain Stochastic Neutral With Distributed Delay

Distributed delay systems are dynamic systems with infinite dimensions described by partial differential equations,integral equations,functional differential equations or differential equations in abstract space,it is widely used in the research of natural science and engineering technology.Neutral system as a special kind of delay differential system,can describe the real problem more accurately.In many practical systems,including heat exchanger,robot contact rigid environment,laser optics,distributed network,lossless transformation line,etc,neutral time-delay systems can be used for mathematical modeling.Therefore,in recent years,more and more attention has been paid to the analysis of neutral systems with distributed delay.In this research,based on the theory of functional differential equations,stability theory,stochastic process and control theory,the mean square exponential stability and robust control of uncertain stochastic neutral systems with distributed delay are studied by using the techniques and methods of integral inequality,interval matrix inequality,Halanay inequality,LMI and Schur complementary lemma.The main research contents are as follows:1.The mean square exponential stability of uncertain stochastic neutral systems with distributed delays is considered.By constructing Lyapunov functional skillfully,using Ito formula,Schur complement lemma,inequality and analysis techniques,some new conditions for the mean square exponential stability of the system are given.Finally,numerical examples are given to illustrate the effectiveness of the method.2.The mean square exponential stability of uncertain stochastic neutral systems with distributed delays under nonlinear perturbations is investigated.In order to overcome the difficulties caused by model transformation and cross term boundary technique,by constructing appropriate Lyapunov functional and introducing auxiliary vector,the stability conditions of a new linear matrix inequality are obtained by using integral inequality and Schur complementary lemma.3.The problem of robust H_? control for uncertain stochastic neutral systems with interval time-varying delay is proposed.By designing a delay dependent robust controller based on LMI,the robust stochastic asymptotic mean square stability of the closed-loop system is guaranteed and the robust performance criteria are satisfied.The comparison with the existing results shows that the sufficient conditions given in this paper are less conservative.4.The problem of robust H_? control for uncertain stochastic neutral systems with distributed delays under nonlinear disturbances is considered.In order to solve the difficulties caused by uncertainties and nonlinear disturbances,a new state feedback controller based on LMI is designed,which not only guarantees the robust stochastic stability of the closed-loop system,but also satisfies the robust performance criteria for all admissible parameter uncertainties.Finally,through a numerical example verify the effectiveness of the proposed method.