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

Zongying Li, Xu Xu*, Tingruo Yan, and Eric Li
International Journal of Control, Automation, and Systems, vol. 20, no. 7, pp.2169-2177, 2022

Abstract : 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 converges 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 the harmonious coexistence of various complex systems within a fixed time interval.

Keyword : Finite time, fixed-time, generalized synchronization, multiplex network, time varying delay.

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