Finite-time synchronization of complex delayed networks via intermittent control with multiple switched periods

In this paper, an intermittent control approach with multiple switched periods is proposed for the finite-time synchronization in complex networks with non-delay and time-varying delay couplings. Based on finite-time stability theory, the theory of Kronecker product of matrices and the inequality techniques, some novel delay-dependent criteria are obtained to ensure finite-time synchronization for the complex networks, which avoid complex computation on the matrix inequalities. Moreover, the convergence time does not depend on control widths and control periods for the proposed intermittent controller with multiple switched periods. When the control width index θ→1-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta \rightarrow 1^-$$\end{document}, the finite-time impulsive synchronization control schemes as special cases are also given. Especially, the traditional synchronization criteria for some models are improved in the convergence time by using the novel periodical intermittent feedback control and the finite-time impulsive control. The results here are also applicable to both directed and undirected weighted networks without any other conditions. Finally, one numerical example with chaotic nodes is given to demonstrate the effectiveness of the proposed controllers.