Researches On Stability And Chaotic Synchronization Of Neural Networks With Time-varying Delay

Neural networks have attracted a lot of attention during recent decades as they have been widely applied to various fields,such as signal processing,pattern recognition,static image processing,associative memory and combinatorial optimization.Because of the limitations in the speed of information processing,the phenomenon of time delay occurs frequently,which usually leads to instability and oscillation in delay neural networks.Therefore,the stability of time-delay neural networks has become a hot research topic.For time-varying delay neural networks,the stability of time-varying delay neural networks is studied in depth by LKF theory,free weight matrix equality and Bessel-Legendre integral inequality,improved second time delay decomposition and linear matrix inequality,and the stability conditions with less conservativeness are obtained.For a class of chaotic neural networks,the master-slave synchronous sampling data control is carried out by combining looped-function method.On the basis of the predecessors,more free weights and non-linear terms are considered,and the sampling period is improved.Some feasible research results are obtained.The main research can be briefly described as follows:(1)For neural networks with time-varying delays,the stability of neural networks with two types of delays depending on whether or not the lower bound of the delay derivative is known is studied.By the improved second time delay decomposition method,two new LKFs are constructed.The free weight matrix equality proposed in this paper is used to replace the previous reciprocal convex combination and the improved reciprocal convex combination.The derivative of LKF is estimated by combining Bessel-Legendre integral inequality.Two stability conditions with less conservativeness are obtained,and the upper bound of time delay is obtained by the obtained conditions which makes the system more fault-tolerant.(2)For chaotic neural networks,master-slave synchronous sampling data control is carried out.A new LKF is constructed by looped-functional technique.The derivative of LKF is estimated by free weight matrix equality and Bessel-Legendre integral inequality.Compared with previous literature,the error system is integrated from sampling time to current time,and several zero terms and positive definite terms are introduced.For the system with or without time delay,two conditions are obtained to make the error system asymptotically stable,and the gain matrices of the sampled controller with larger sampling period are obtained by the stability conditions.The simulation results show the method is effective.Finally,the work done in this paper is summarized,and some problems and further development directions in the theoretical research of time-delay neural networks are pointed out,and the future research work is prospected.