Intermittent Control for Cluster-Delay Synchronization in Directed Networks

Abstract

We investigate cluster-delay synchronization of a directed network possessing cluster structures by designing an intermittent control protocol. Based on Lyapunov stability theory, we proved that synchronization can be realized for oscillators in the same cluster and cluster-delay synchronization can be realized for the whole network. By simplifying the obtained sufficient conditions, we carry out a succinct and utilitarian corollary. In addition, comparative researches are carried out to show the differences and the usefulness of the obtained results with respect to other similar controllers from the recent literature. Finally we provide two numerical examples to show the effectiveness of the control schemes.

Synchronization of fractional-order dynamical network via aperiodically intermittent pinning control

“…Zhou et al [16] studied the exponential lag synchronization for neural networks with mixed delays via intermittent control. Zhang et al [17] considered the intermittent control for clusterdelay synchronization in directed networks. He et al [23] investigated the exponential synchronization of dynamical network with distributed delays via intermittent control.…”

Parameter Identification and Adaptive Control of Uncertain Goodwin Oscillator Networks with Disturbances

“…From the viewpoint of mathematics, the core of synchronization is the stability of the zero solution of network error systems [14][15][16]. In previous studies, two effective methods are usually employed: the first one is to study synchronization induced by the mutual couplings between nodes [17,18], and the second one is to design reasonable control laws [19][20][21]. A great number of researches on the first method have indicated that synchronization without external control needs certain requirement in both network structures and node dynamics.…”