Finite-Time Anti-Synchronization Of A Class Of Dynamical Systems With Bounded Time-Varying Delays

Based on the dynamical characteristics of the master-slave systems,this paper investigates the anti-synchronization problems of a class of dynamical systems with time-varying delays and proves that under certain conditions,the systems can achieve the anti-synchronization in a finite time.In fact,by classifying the initial anti-synchronization errors of the systems,this paper proposes two new control strategies to investigate the anti-synchronization process of the systems respectively: when the absolute value of the initial errors of the system are greater than 1,by constructing M-function and rigorous analysis,it shows that the absolute value of the errors will be equal to 1 after a finite time;then,with the help of H(?)lder inequality and some analysis techniques,we can get that the antisynchronization errors will be equal to 0 after a fixed time.By synthesizing the two control strategies,it can be concluded that for any initial values,the state vectors of the master-slave systems will eventually achieve finite-time antisynchronization.It is worth mentioning that these new control strategies proposed in this paper are only related to the current state of the systems,but not to the time delays.The control strategies are more flexible than the time-delay related control strategies proposed in the previous literature,and easier to operate in practice.In the end of this paper,we illustrate some numerical simulations to verify our conclusions.