Stability Analysis Of Impulsive Neural Networks With Impulsive Time Window

Artificial neural network,which consists of a large number of interconnected processing units,is a nonlinear and adaptive information processing system.It has been widely used in pattern recognition,image processing and nonlinear optimization,et al.In order to describe the instantaneous change of system state,impulse neural networks have been proposed,and a lot of theoretical studies have been carried out.So far,most theoretical studies of impulsive system focused on the impulsive system with fixed-time impulses.However,in most practical impulsive systems,the time of impulse occurrence is almost unpredictable,or time-varying.But due to the complexity of theoretical analysis,study on the case of time-varying impulses is still at initial stage.This paper studies the qualitative theory of impulsive neural networks with time-varying impulses.In order to simplify the analysis,we assume that the impulse instant is limited to a time interval,i.e.,every impulse instant is uncertain,but the impulse does occur in a certain time interval.We call this time interval the impulse time window.In this paper,an impulsive neural network model with impulse time window is established,and the stability of these impulsive neural network models is analyzed.A series of sufficient conditions for ensuring the asymptotic stability of the system are obtained.The main contents and contributions of this thesis are as follows:1.The linear impulsive system model with impulse time window is established,and its stability is studied.The sufficient conditions of asymptotically stability are obtained.2.Impulse time window is introduced into delayed neural network model,and then the exponential stability of proposed neural network model with impulse time window is studied,and the constraint relationship between the exponential convergence rate and the parameters in the impulse time window is proposed.The validity of the theoretical results is verified by numerical simulations.3.Impulse time window is introduced into switched neural networks.We set up a class of more general hybrid impulsive switching neural network model,and obtain some sufficient conditions for the exponential stability of the model through theoretical analysis.Numerical simulations are given to verify the validity of the theoretical analysis.