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This book deals with the stabilization issue of infinite
dimensional dynamical systems both at the theoretical and
applications levels. Systems theory is a branch of applied
mathematics, which is interdisciplinary and develops activities in
fundamental research which are at the frontier of mathematics,
automation and engineering sciences. It is everywhere, innumerable
and daily, and moreover is there something which is not system: it
is present in medicine, commerce, economy, psychology, biological
sciences, finance, architecture (construction of towers, bridges,
etc.), weather forecast, robotics, automobile, aeronautics,
localization systems and so on. These are the few fields of
application that are useful and even essential to our society. It
is a question of studying the behavior of systems and acting on
their evolution. Among the most important notions in system theory,
which has attracted the most attention, is stability. The existing
literature on systems stability is quite important, but disparate,
and the purpose of this book is to bring together in one document
the essential results on the stability of infinite dimensional
dynamical systems. In addition, as such systems evolve in time and
space, explorations and research on their stability have been
mainly focused on the whole domain in which the system evolved. The
authors have strongly felt that, in this sense, important
considerations are missing: those which consist in considering that
the system of interest may be unstable on the whole domain, but
stable in a certain region of the whole domain. This is the case in
many applications ranging from engineering sciences to living
science. For this reason, the authors have dedicated this book to
extension of classical results on stability to the regional case.
This book considers a very important issue, which is that it should
be accessible to mathematicians and to graduate engineering with a
minimal background in functional analysis. Moreover, for the
majority of the students, this would be their only acquaintance
with infinite dimensional system. Accordingly, it is organized by
following increasing difficulty order. The two first chapters deal
with stability and stabilization of infinite dimensional linear
systems described by partial differential equations. The following
chapters concern original and innovative aspects of stability and
stabilization of certain classes of systems motivated by real
applications, that is to say bilinear and semi-linear systems. The
stability of these systems has been considered from a global and
regional point of view. A particular aspect concerning the
stability of the gradient has also been considered for various
classes of systems. This book is aimed at students of doctoral and
master's degrees, engineering students and researchers interested
in the stability of infinite dimensional dynamical systems, in
various aspects.
This book deals with the stabilization issue of infinite
dimensional dynamical systems both at the theoretical and
applications levels. Systems theory is a branch of applied
mathematics, which is interdisciplinary and develops activities in
fundamental research which are at the frontier of mathematics,
automation and engineering sciences. It is everywhere, innumerable
and daily, and moreover is there something which is not system: it
is present in medicine, commerce, economy, psychology, biological
sciences, finance, architecture (construction of towers, bridges,
etc.), weather forecast, robotics, automobile, aeronautics,
localization systems and so on. These are the few fields of
application that are useful and even essential to our society. It
is a question of studying the behavior of systems and acting on
their evolution. Among the most important notions in system theory,
which has attracted the most attention, is stability. The existing
literature on systems stability is quite important, but disparate,
and the purpose of this book is to bring together in one document
the essential results on the stability of infinite dimensional
dynamical systems. In addition, as such systems evolve in time and
space, explorations and research on their stability have been
mainly focused on the whole domain in which the system evolved. The
authors have strongly felt that, in this sense, important
considerations are missing: those which consist in considering that
the system of interest may be unstable on the whole domain, but
stable in a certain region of the whole domain. This is the case in
many applications ranging from engineering sciences to living
science. For this reason, the authors have dedicated this book to
extension of classical results on stability to the regional case.
This book considers a very important issue, which is that it should
be accessible to mathematicians and to graduate engineering with a
minimal background in functional analysis. Moreover, for the
majority of the students, this would be their only acquaintance
with infinite dimensional system. Accordingly, it is organized by
following increasing difficulty order. The two first chapters deal
with stability and stabilization of infinite dimensional linear
systems described by partial differential equations. The following
chapters concern original and innovative aspects of stability and
stabilization of certain classes of systems motivated by real
applications, that is to say bilinear and semi-linear systems. The
stability of these systems has been considered from a global and
regional point of view. A particular aspect concerning the
stability of the gradient has also been considered for various
classes of systems. This book is aimed at students of doctoral and
master's degrees, engineering students and researchers interested
in the stability of infinite dimensional dynamical systems, in
various aspects.
This book describes recent developments in a wide range of areas,
including the modeling, analysis and control of dynamical systems,
and explores related applications. The book provided a forum where
researchers have shared their ideas, results on theory, and
experiments in application problems. The current literature devoted
to dynamical systems is quite large, and the authors' choice for
the considered topics was motivated by the following
considerations. Firstly, the mathematical jargon for systems theory
remains quite complex and the authors feel strongly that they have
to maintain connections between the people of this research field.
Secondly, dynamical systems cover a wider range of applications,
including engineering, life sciences and environment. The authors
consider that the book is an important contribution to the state of
the art in the fuzzy and dynamical systems areas.
This book describes recent developments in a wide range of areas,
including the modeling, analysis and control of dynamical systems,
and explores related applications. The book provided a forum where
researchers have shared their ideas, results on theory, and
experiments in application problems. The current literature devoted
to dynamical systems is quite large, and the authors' choice for
the considered topics was motivated by the following
considerations. Firstly, the mathematical jargon for systems theory
remains quite complex and the authors feel strongly that they have
to maintain connections between the people of this research field.
Secondly, dynamical systems cover a wider range of applications,
including engineering, life sciences and environment. The authors
consider that the book is an important contribution to the state of
the art in the fuzzy and dynamical systems areas.
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