The Synchronicity Analysis Of Impulsive Delay Neural Network System

As a typical control system, impulse delayed neural network systemwidely consist in the many motion process of modern science technologyand engineering field, and the control theory and application in the controlengineering is still in the developing. The exist of the delay and impulseoften lead to the control performance of the system unstable, impulsecontrol as a kind of easy realization, low cost, low consumption controlmethod can make the system performance stable, so for the research of theimpulse delayed system has extensive practical background andapplication value. The main job of the paper as follows:(1) For the robust synchronization problem of a class of neuralnetwork with S-distribution delay and impulsive control a criterion toguarantee the system robust synchronization is established. The uncertainnonlinear coupling function was introduced to this kind of neural network,through structure suitable Lyapunov function and use some inequalityanalysis technology, the robust synchronous properties of such impulsedelayed neural network is studied, and a practical conditions is obtained toguarantee that the network has the general impulse robust synchronization. (2) Based on the average impulse occurring interval concept, theglobal exponential stability problem of a class of mixed impulse geneticnetwork is studied, and the criterion is given to guarantee that the geneticnetwork global exponential stability. A new concept named as averageimpulsive occurring interval is introduced for the first time to describe thefrequency of impulsive effects by referring to the concept of average dwelltime used in the switched system, the definition method of the stabilizingimpulsive and destabilizing impulsive was put forward, then based on theLyapunov stability theory, the criterion is concluded to ensure that thiskind of genetic network global exponential stability, and the impulsecontrol method to guarantee system stability is obtained.(3) A kind of time-varying delay impulse coupled neural networkmodel is presented, where the impulse intensity is time–varying, and theglobal exponential synchronization problem of this kind neural networkmodel is studied. Take the stabilizing impulse and destabilizing impulseinto account at the same time, combined with the average impulseoccurring interval concept and impulse type Halanay inequality approach,the criterion to guarantee the impulsive delayed coupling system globalexponential synchronization is established, and the design method of the impulse controller is obtained. At the same time the criterion of globalexponential synchronization of the network without delay is considered,these results provide a new method for the global exponentialsynchronization of time-varying delayed coupling system.