Synchronization Analysis Of Complex Dynamic Networks With Saturated Impulses

As one of the most basic dynamic behaviors of complex networks,synchronization has been widely used in secure communication,formation control,robot control and so on.Impulse control has the advantages of low cost,easy realization and good control effect,so it is often used as a control method in the study of complex network synchronization.At present,the theoretical achievements of impulse control mainly focus on the fixed-time impulse,and the research on the variable-time impulse(state-dependent impulse)is still relatively few.However,in real life,the time of impulse occurrence is not fixed,and the impulse actuator will be saturated due to the limitations of physical equipment.Therefore,the research of variable-time impulse controller with saturation constraint has important theoretical significance and application value.In this paper,we mainly study the synchronization of complex networks with saturation constraints under state-dependent impulse control and the saturation impulse synchronization of complex dynamic networks with double delay.The specific content and major contributions are as follows:1.The synchronization problem of complex networks with saturation constraints under state-dependent impulse control is studied.Firstly,by constraining the impulse rule,a sufficient condition is given for the trajectory of the synchronization error system intersects each impulse plane exactly once,so as to avoid Zeno phenomenon.Then the state-dependent impulse error system is simplified to a fixed-time impulse error system by using the B-equivalent method.Then,the saturated term is transformed into a series of linear combinations by using convex analysis.The sufficient conditions for local synchronization of complex networks are obtained by means of mathematical induction and inequality techniques.Based on the comparison principle and Lyapunov stability theory,some new impulse global synchronization criteria are proposed.The results show that the complex dynamic networks can achieve synchronization under the control of a statedependent impulse controller with saturation constraints when the appropriate conditions are satisfied.2.The problem of saturation impulse synchronization for complex dynamic networks with double time delay is studied.Under the condition that the system itself has time delay and the nodes in the complex network have time delay in information interaction,the linear feedback controller and the impulse controller are designed,and the appropriate Lyapunov functions are established.Then,by using the generalized Barbalat lemma and inequality techniques,the sufficient conditions for global asymptotic synchronization of the complex network are obtained.Finally,the validity of the synchronization criterion is verified by two numerical simulations.