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Title:  Synchronization and consensus analysis of complex networks 
Other Titles:  Fu za wang luo de tong bu he yi zhi xing fen xi 複雜網絡的同步和一致性分析 
Authors:  Xiong, Wenjun ( 熊文軍) 
Department:  Department of Mathematics 
Degree:  Doctor of Philosophy 
Issue Date:  2010 
Publisher:  City University of Hong Kong 
Subjects:  Computer networks  Management. Synchronization. 
Notes:  CityU Call Number: TK5105.5 .X56 2010 ix, 140 leaves 30 cm. Thesis (Ph.D.)City University of Hong Kong, 2010. Includes bibliographical references (leaves [122]140) 
Type:  thesis 
Abstract:  The last decade has witnessed the birth of a new movement of interest and research in
the study of complex networks, i.e. networks whose structure is irregular, complex and
dynamically evolving in time. The main focus has moved from the analysis of small
networks to that of systems with thousands or millions of nodes, with a renewed attention
to the properties of networks of dynamical units. This flurry of activity, triggered
by two seminal papers, that by Watts and Strogatz on smallworld networks, appeared
in Nature in 1998, and that by Barabási and Albert on scalefree networks appeared
one year later in Science, has seen the physics' community among the principal actors,
and has been certainly induced by the increased computing powers and by the
possibility to study the properties of a plenty of large databases of real networks.
The research on complex networks begun with the effort of defining new concepts
and measures to characterize the topology of real networks. The main result has been
the identification of a series of unifying principles and statistical properties common to
most of the real networks considered. Over the past decade, much of the interesting dynamical
behavior of complex dynamical networks, such as synchronization, consensus
and spatiotemporal chaos, has recently attracted increasing attention from researchers
in different areas. Among these, synchronization and consensus techniques have been
applied in many fields, such as secure communication, harmonic oscillation generation
and parallel image processing. Hence, synchronization and consensus analysis for complex networks has important reallife application.
The major work of this thesis is to analyze synchronization and consensus of complex
networks. In Chapter 2, due to the fact that we usually have to consider some
algebraic constraints of complex networks in modeling the real world problems, we
aim to build singular hybrid coupled systems to describe complex networks with a
special class of constraints. Based on a reference state and the Lyapunov stability, a
sufficient condition is obtained ensuring the globally asymptotical synchronization of
a class of singular hybrid coupled networks with finitevarying nonlinear perturbation.
In Chapter 3, pinning synchronization of a directed network with Markovian jump
and nonlinear perturbations is considered. By analyzing the structure of the network, a
detailed pinning scheme is given to ensure the synchronization of all nodes in a directed
network. This pinning scheme can overcome the difficulties of deciding which nodes
needs to be pinned. This scheme can also identify the exact least number of pinned
nodes for a directed network model. In addition, the timevarying polytopic directed
network with Markovian jump is discussed.
In Chapter 4, the consensus problem of multiagent nonlinear directed networks
is discussed in the case that a multiagent nonlinear directed network does not have a
spanning tree to reach the consensus of all nodes. By using the Lie algebra theory, a
linear nodeandnode pinning method is proposed to achieve a consensus for all nonlinear
functions satisfying a given set of conditions. Based on some optimal algorithms,
largesize networks are aggregated to smallsize ones. Subsequently, by applying the
principle minor theory to the smallsize networks, a sufficient condition is given to
reduce the number of controlled nodes.
In Chapter 5, the consensus problem of a multiagent directed network with nonlinear
perturbations is investigated. Based on a reducedorder transformation, it is
shown that the discussed multiagent model cannot reach a consensus under a Hypoth esis even though the discussed network has a spanning tree. An impulsive approach
is then introduced and a simple criterion is presented to guarantee the consensus of all
agents in the multiagent model. 
Online Catalog Link:  http://lib.cityu.edu.hk/record=b4086906 
Appears in Collections:  MA  Doctor of Philosophy

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