Stability Analysis Of Networks Model Under Impulsive Control Strategy

Neural network is a nonlinear system with complex of dynamic behavior.After continuous development and improvement,it has been successfully applied to artificial intelligence,computer science,image processing and other scientific fields.Due to its small control volume and low control cost,impulsive control has attracted wide attention from scholars in recent years.In particular,the stability of impulsive neural networks has been studied in depth.However,the impulsive strategy of neural networks on the time scale and high-order neural networks has not yet received sufficient attention,related work needs to be further deepened.On the basis of the existing results,this article studies the stability of several types of neural networks,including three aspects:(1)The multi-agent impulse signal was introduced to study the consensus problem of nonlinear second-order multi-agents.The impulsive controlled protocol with time-delay effects was designed to obtain the consensus of the second-order multi-agent system with fixed network topology.The result was extended to second-order multi-agent systems with switched network topology.(2)The exponential stability of the impulsive neural network with delays on the time scale is studied.Using the Razumikhin technique and the Lyapunov function,the sufficient conditions for the time-delay impulsive network system to achieve exponential stability on the time scale are given.It provides a method to study the continuous system and the discrete system at the same time,which reduces the limitation on the stability of neural networks.(3)The problem of exponential stability of a class of Hopfield-type impulsive neural networks under impulsive effects is studied.By using the method of Lyapunov function,the Hopfield-type impulsive neural network is constructed to achieve sufficient conditions for exponential stability.It provides a new idea and reference basis for studying the impulsive system with unbounded time delay.