Fixed-time synchronization of complex dynamical network with impulsive effects

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 Holder 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.