Fixed-time Synchronization in the Delayed Multiplex Networks by the Auxiliary-system Approach

摘要

This paper investigates the generalized synchronization of the multiplex networks with time varying delay by using the auxiliary-system approach. A delay-dependent controller is first proposed by adding feedback interactions between the response and auxiliary networks. With the fixed-time synchronization theory, the controlled systems can achieve generalized synchronization where the error between the response and auxiliary networks converge exactly to zero in a finite amount of time that is independent of the initial condition. In addition, a delay-independent control law is also designed to decrease the control complexity. This work provides engineers a convenient approach to realize harmonious coexistence of various complex systems within the fixed time interval.