Research Article
Further Results on Sampled-Data Synchronization for Complex
Dynamical Networks with Time-Varying Coupling Delay
Hea-Min Lee ,
1
Wookyong Kwon ,
1
Sangmoon Lee ,
2
and Dongyeop Kang
1
1
Smart Vehicles Laboratory, Electronics and Telecommunications Research Institute, Daegu 42994, Republic of Korea
2
School of Electronics Engineering, Kyungpook National University, Daegu 41566, Republic of Korea
Correspondence should be addressed to Sangmoon Lee; moony@knu.ac.kr
Received 5 September 2018; Revised 7 November 2018; Accepted 12 November 2018; Published 26 November 2018
Guest Editor: Hiroaki Mukaidani
Copyright © 2018 Hea-Min Lee et al. Tis is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Tis paper deals with the sampled-data synchronization problem for complex dynamical networks (CDNs) with time-varying
coupling delay. To get improved results, two-sided free-weighting stabilization method is utilized with a novel looped functional
taking the information of the present sampled states and next sampled states, which can more precisely account for the sawtooth
shape of the sampling delay. Also, the quadratic generalized free-weighting matrix inequality (QGFWMI), which provides
additional degree of freedom (DoF), is utilized to calculate the upper limit of the integral term. Based on the novel looped functional
and QGFWMI, improved conditions of stability are derived from forms of linear matrix inequalities (LMIs). Te numerical
examples show the validity and efectiveness.
1. Introduction
Complex dynamical networks (CDNs) are an attempt to
model a set of interconnected dynamic properties of nodes
with specifc contents. For example, there are human interac-
tion networks, ad hoc networks, secure communications, har-
monic oscillations, biological systems, and chaotic systems,
fnancial systems, social networks, and neural networks.
CDNs are faced with the problems of expressing struc-
tural complexity and connection diversity at the same time.
Furthermore, the dynamic characteristics of the network
make it difcult to provide a solution to the real world
because modeling should be done with the node’s insufcient
information from the network. Nevertheless, CDNs have
attracted lots of attention in various felds of engineering
[1–4]. Especially, the problem of synchronization has been
focused by many researchers [5–7], as the synchronization
of CDNs is a fundamental phenomenon. In nature, complex
networks in the synchronization encounter time delay in
biological and physical networks, because of the limited speed
of network transmission, trafc jams, and signal propagation.
Te time delay is a source of degradation synchronization
performance and instability, and thus complex networks with
time-varying delay are of importance and generality [8, 9].
Te design of control has been developed including pin-
ning control [10], impulsive control [11], hybrid control [12],
fuzzy adaptive output feedback control [13], and sampled-
data control [5] to accomplish stable synchronization. Among
these methods, sampled-data control for the synchronization
of CDNs has been studied extensively with the develop-
ment of digital communication since sampled-data ofers
many benefts in modern control systems. Te advantages
of sampled-data control are as follows: Firstly, the sampled-
data control is more realistic than continuous control in
that it can be implemented in practical systems. Secondly,
in the case of the signal in the form of pulse data, the
information is supplied immediately with a small outlay.
Lastly, the control system for better performance is generally
achieved by a sampled-data control. For continuous systems,
the diferentiator not only improves the existing noise but also
generate additional noise. In the sampled-data system, the
diferential operation can be implemented without increas-
ing noise problem. For that reason, sampled-data control
was used because of these benefts: practicality, immediacy,
economics, and accuracy. In sampled-data control systems,
it is the main issue to design controllers that can get larger
sampling interval. Increasing maximum sampling interval is
very important because it not only enlarges the stable region
Hindawi
Mathematical Problems in Engineering
Volume 2018, Article ID 4931658, 11 pages
https://doi.org/10.1155/2018/4931658