چكيده به لاتين
Complex dynamical networks, which include a large number of interconnected nodes, are one
of the prominent issues that receive extensive attention due to its universality in the nature or
man-made systems. Among various phenomena in these networks, synchronization has attracted
great attention in recent studies as an important subject in collective behaviors of complex
dynamical networks. Synchronization means that the state vectors of all the nodes in a complex
dynamical network converge to a unified behavior as a common state vector. Various factors
threaten synchronization that reduce the efficiency of complex dynamical networks. In this
thesis, we try to look at the issue of synchronization problem in the presence of challenges. The
main purpose of this study is synchronization investigation of delayed complex dynamical
networks in which the network structure is changing abruptly in a finite dimensional
probabilistic space due to faults in different parts of the network. Such structures can be modeled
by Markov jump systems whose its main characteristic is transition rate values which govern
switches between the different modes and determine the behavior of the system. Although it is
very idealistic to get the accurate and complete transition rate information due to the difficulty
or the costs of measuring the transition rates, the transition rates in a Markov process are
assumed uncertain.
One class of uncertain transition rate classes is time-varying transition rates that reduces the
limitations of the Markov process. One of the popular solutions for solving Markov process with
time varying transition rates (non-homogeneous Markov process) is to consider transition rates
as piecewise-constant. In other words, in this way, the non-homogeneous Markov process can
be considered as piecewise-homogeneous Markov process. In actual networks due to signal
propagation limitations among the units in a network or traffic congestion; the time delay is an
undeniable part in practical systems that causes instability or oscillation; hence, a wide variety
of methods is used to study the time delay. The purpose of this study is to achieve a maximum
delay to reduce conservatism while the synchronization is maintained. This thesis is organized
in 6 chapters. In two first chapters, we discuss basic concept of complex dynamical networks,
synchronization problem and so on. The synchronization problem of a Markovian Jump
complex dynamical networks with constraint are studied in chapter 3, 4 and 5. All of the
synchronization criteria are derived by Lyapunov-Krasovskii functional method and expressed
in terms of linear matrix inequities to obtain the controller gain matrices in each chapter.
The effectiveness of the proposed method in each section is illustrated by numerical examples
in simulation results in each chapter. A network of three coupled Chua's circuits is used as a
numerical example in this thesis.
