Qualitative Analysis Of Several Kinds Of Time-delay Systems

This thesis mainly studies the stability of time-varying delay neural net-works.By constructing an appropriate Lyapunov-Krasovskii functional and using the improved integral inequality and matrix inequality technology,a simple and ef-fective stability criterion with low conservatism is given in the form of linear matrix inequality.First,static neural networks with interval time-varying delays are studied,the weak conditions 0≤r₁≤r（t）≤r₂及|（?）（t）|≤v are considered,by introducing more time-delay state term information and new augmented vector,the correspond-ing augmented LKF is obtained,which can better segment the time-delay of neural network system,make full use of the correlation between integral terms,reduce the conservatism of stability criteria,and obtain a larger upper bound of delay.Secondly,neural networks with time-varying delays are studied,A new Lyapunov-Krasovskii functional with non positive definite is constructed,and the square of delay in the functional derivative is treated by using the convexity of quadratic function.The positive definiteness of the newly constructed Lyapunov-Krasovskii functional does not require that all symmetric matrices are positive definite,which makes the stability determination condition of neural network system more relaxed,so that the obtained delay criterion has less conservatism.Then generalized neural networks with time-varying delays are studied,based on the given Lyapunov-Krasovskii functional,and（?）（t）≤v≤1 to（?）（t）≤v,a new sufficient condition for asymptotic stability of delayed neural networks is established,and a larger delay upper bound is obtained.In the end,briefly summarizes the research work of this paper and looks forward to the future research direction.4 picture,8 tables,70 references.