Research Article
Networked Convergence of Fractional-Order Multiagent
Systems with a Leader and Delay
Yuntao Shi
1
and Junjun Zhang
2
1
Key Laboratory of Beijing for Field-Bus Technology & Automation, North China University of Technology, Beijing 100144, China
2
College of Science, North China University of Technology, Beijing 100144, China
Correspondence should be addressed to Yuntao Shi; shiyuntao@ncut.edu.cn
Received August ; Accepted October
Academic Editor: Michael Z. Q. Chen
Copyright © Y. Shi and J. Zhang. is 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.
is paper investigates the convergence of fractional-order discrete-time multiagent systems with a leader and sampling delay by
using Hermite-Biehler theorem and the change of bilinearity. It is shown that such system can achieve convergence depending on
the sampling interval , the fractional-order ,andthesamplingdelayand its interconnection topology. Finally, some numerical
simulations are given to illustrate the results.
1. Introduction
Recently, more and more scholars focus on the coordinated
control [, ] of multiagent systems such as the consensus [–
] and the controllability [–]. However, most of the practi-
cal distribution systems are fractional order [–]. Recently,
with the development of society, fractional-order calculus
theory [–] is widely used to study the signal processing
and control, picture processing and articial intelligence,
and so on. e consensus of multiagent systems refers to
thefactthatagentsinthesystemcantransferinformation
and inuence each other according to a certain protocol or
algorithm, and eventually agents will tend to the consensus
behavior with the evolution of the time in []. In fact, for
most of multiagent systems, there widely exist time delays as
in []. So the property of multiagent systems with time delays
has always been the hot problem. In [], the authors studied
consensus of multiagent systems with heterogeneous delays
and leader-following with integer-order and continuous time.
In [], the paper considered the consensus of fractional-
order multiagent systems with sampling delays without the
leader.
However, for a complex environment, multiagent systems
with fractional-order can be better to describe some real
natural phenomena. Some basic issues of fractional-order
multiagent systems with time delay, such as the convergence,
arestilllackinginstudying.Specially,forafractional-order
multiagent system, which depends crucially on sampling
interval , the fractional-order ,anditsinterconnection
topology, therefore, it is more dicult to study the conver-
gence of the fractional-order multiagent system.
In this paper, we consider the convergence of fractional-
order discrete-time multiagent systems with a leader and
sampling delay. e leader plays the role of an external input
or signal to followers, and the followers update their states
basedontheinformationavailablefromtheirneighborsand
the leader. We will establish convergence conditions and
discuss relations among sampling interval , the fractional-
order ,itssamplingdelay,anditsinterconnectiontopology
of such network.
e remainder of this paper is organized as follows.
Section gives the model and some preliminaries. Section
presents the main results, and some simulations are given in
Section . Finally, Section gives the conclusion.
2. Preliminaries and Problem Statement
In this section, we introduce some useful concepts and
notations about the denition of fractional derivative [],
graph theory, and convergence of the multiagent systems.
Hindawi Publishing Corporation
Mathematical Problems in Engineering
Volume 2015, Article ID 314985, 6 pages
http://dx.doi.org/10.1155/2015/314985
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