Stability And Synchronization Analysis Of Nonlinear Systems Based On Event-triggered Impulsive Controls

Due to the influence of human,environment and other interference factors,most systems are nonlinear in practical application,ignoring the nonlinear factors in the systems and only studying the linear part will reduce systems’ universality.As the rapid development of engineering technology and computer technology,the linear systems with poor universality can not meet the increasing performance requirements of the systems,which promote the research of nonlinear systems.Due to these advantages in improving system robustness,saving energy and reducing information redundancy,event-triggered impulsive control(ETIC)has become a research hotspot of scholars in various fields.However,most of the existing results are limited to the research of ETIC in the identical linear system,and there are few research results for the more practical nonlinear systems and nonlinear parameter mismatch systems.In order to make up for the shortcomings of the existing results,this paper studies the stability and synchronization of nonlinear systems based on ETIC,Lyapunov stability theory and comparison principle of impulsive systems.The main contents include:1.The ETIC method in which the impulsive instants are updated based upon the event trigger conditions is designed,the stability of nonlinear systems under this control method is studied.Firstly,we proved that the systems are no Zeno behavior under the designed ETIC.Secondly,sufficient conditions for the systems to be exponential stable to the origin are obtained.2.The synchronization problem of nonlinear drive-response systems under ETIC is studied.On the one hand,we proved that the Zeno behavior can be eliminated in the controlled systems.On the other hand,sufficient conditions for the systems to achieve exponential synchronization are obtained.3.The quasi-synchronization problem of nonlinear parameter mismatched drive-response systems is researched based on ETIC.It is proved that there is no Zeno behavior in the systems,sufficient conditions for the systems to achieve quasi-synchronization and the synchronization error bound are given.4.Two kinds of triggered mechanisms,that is,the centralized event-triggered impulsive control(CETIC)and the distributed event-triggered impulsive control(DETIC)are designed respectively for the nonlinear heterogeneous network systems with directional communication topology.Sufficient conditions for the systems to achieve quasi-synchronization and the corresponding synchronization error bounds are obtained,what is more,the Zeno behavior is shown to be excluded.In addition,the simulation results show that DETIC has more advantages in reducing the nodes’ information interaction and improving the utilization of system resource.