Finite-time synchronization of multi-layer nonlinear coupled complex networks via intermittent feedback control

Abstract

This paper addresses the problem of finite-time synchronization for a class of multi-layer nonlinear coupled complex networks via intermittent feedback control. Firstly, based on finite-time stability theory, some novel criteria are given to guarantee that the error system of drive-response systems is still finite-time stable under an inherently discontinuous controller. Then, by proposing two kinds of intermittent feedback control laws, sufficient conditions of finite-time synchronization of two kinds of multi-layer complex networks are derived, respectively. The time delay between different layers is also taken into consideration. Finally, a numerical example is provided to verify the effectiveness of the proposed methods. Index Terms Complex networks, finite-time synchronization, multi-layer, intermittent feedback control. I. I In the past few decades, the synchronization problem of complex networks has attracted more and more attention in practical applications [1], [2], [3], [4], [5], [6]. A basic complex network consists of some nodes and links between the nodes, where each node is a dynamic system. Since the problem of synchronization of chaotic systems has been studied in [1], synchronization as a potential engineering application has been applied into secure communication, neural network, biology and information processing [7], [8], [9], [10], [11]. Up till now, there are lots of different types of synchronization, for instance, complete synchronization [12], anti-synchronization [13], projective synchronization [14] and cluster synchronization [15], [16]. It should be noted that information of different nodes is transmitted based on a shared band-limited digital communication network. Thus, it is interesting to study synchronization of complex networks with delayed coupling. For example, global synchronization of a general linear coupled network has been studied with a time-varying coupling delay in [17]. Then, a developed generalized mixed outer synchronization are also studied with a time-varying coupling delay [18]. In [19], local and global synchronization of complex networks have been studied with a fixed delay. In [20], global exponential synchronization of

Finite-time synchronization of uncertain complex dynamic networks with time-varying delay

“…The nonlinear coupling is ubiquitous in most practical systems. Several scholars have investigated the nonlinear coupling between various factors within the node [10,15,16,27,28].…”

“…The finite and fixed time synchronization of complex networks with delay were evaluated in [14]. Finite-time synchronization of multi-layer nonlinear complex networks was achieved by using intermittent feedback control in [15], and linear complex networks were assessed under the same state in [36]. The problem of adaptive finite-time outer synchronization between two complex networks was solved in [37].…”

“…In practical systems, uncertainty is ubiquitous. For systems without uncertainty, such as model (15), system instability may occur given the changes in controller parameters. Here, we investigate the finite-time synchronization problem of system (15) by using a non-fragile controller (21).…”

“…Here, we investigate the finite-time synchronization problem of system (15) by using a non-fragile controller (21). (15), under Assumptions 1 and 2, if positive-definite symmetric matrices K i , P i , S i and Q i exist, so that…”

“…Li et al [14] realized the synchronization of finite and fixed time delays of a complex dynamic network simultaneously by designing a new controller and using aperiodic intermittent control and obtained several sufficient conditions for system synchronization through eigenvalue characterization. Zhang and Shen et al [15] proposed several new criteria that can ensure multiple complex systems to achieve finite-time synchronization under periodic or aperiodic discontinuous controllers. Li et al [16] obtained several sufficient conditions for finite-time synchronization of nonlinearly coupled networks with time-varying delay by performing a new analysis.…”