Input-to-State Stability Of Reaction-Diffusion Neural Networks

The reaction-diffusion neural networks model have extensive applications,such as image processing,signal processing,optimization and so on.In practice,the control systems are easy to be affected by external interference.Therefore,this requires that the control system not only be stable,but also be input-to-state stability.In this paper,the input-to-state stability of reaction-diffusion neural network is studied.The specific research contents are introduced in the following two aspects.In this section,we primarily investigate input-to-state stability of reaction-diffusion neural networks with time delay,in which the active function isn' t required to be smooth and bounded.By using Lyapunov functions and utilizing delay differential inequality with time-varying input,several input-to-state stability sufficient conditions are derived for reaction-diffusion neural networks.This section mainly concern with input-to-state stability of impulsive delayed reaction-diffusion neural networks.Firstly,a model of reaction-diffusion neural network with time-varying delays and impulsive effects is formulated,in which impulsive func?tions are nonlinear.On the basis of existing document,a more generalized impulsive and time-delay differential inequality lemma is given,the conclusion of reaction-diffusion neural networks with impulsive is obtained.Further,it also shows how the impulsive can make the reaction-diffusion neural network achieve input-to-state stability.The present approach can remove some conservative and restrictive conditions on input-to-state sta-bility given in existing publication.