Abstract
Fixed-time synchronization of complex dynamical networks with impulsive effects is investigated in this paper. First of all, a novel lemma about the fixed-time stability of the impulsive dynamical system is proposed, in which the settling time is regardless of the initial values of the considered system. Secondly, by constructing a Lyapunov function made up of the error states' 1-norm, we design a unified controller for the network to achieve synchronization within the settling time. Moreover, the convergence time given in this paper is more accurate than that in some existing literatures. Furthermore, the nonlinear term of the dynamical behavior is assumed to be Hölder continuous, which is more general than the common Lipschitz condition. Finally, a numerical example is provided to illustrate the correctness and the effectiveness of the main result.
Highlights
Recent years have witnessed an increasing interest in complex networks on account of its wide applications [1]–[4], such as electrical power grids, biological networks, communication networks and so on
Yang et al studied the fixed-time synchronization of complex dynamical networks with impulsive effects via non-chattering control in 2017 [25]
(2) A unified controller is designed to that the synchronization of the impulsive dynamical network can be reached within a settling time, which is regardless of the initial values of the considered system
Summary
Recent years have witnessed an increasing interest in complex networks on account of its wide applications [1]–[4], such as electrical power grids, biological networks, communication networks and so on. INDEX TERMS Fixed-time synchronization, complex dynamical networks, impulsive effects, control. N. Li et al.: Fixed-Time Synchronization of Complex Dynamical Network With Impulsive Effects
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