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This book provides the mathematical foundations of networks of
linear control systems, developed from an algebraic systems theory
perspective. This includes a thorough treatment of questions of
controllability, observability, realization theory, as well as
feedback control and observer theory. The potential of networks for
linear systems in controlling large-scale networks of
interconnected dynamical systems could provide insight into a
diversity of scientific and technological disciplines. The scope of
the book is quite extensive, ranging from introductory material to
advanced topics of current research, making it a suitable reference
for graduate students and researchers in the field of networks of
linear systems. Part I can be used as the basis for a first course
in Algebraic System Theory, while Part II serves for a second,
advanced, course on linear systems. Finally, Part III, which is
largely independent of the previous parts, is ideally suited for
advanced research seminars aimed at preparing graduate students for
independent research. "Mathematics of Networks of Linear Systems"
contains a large number of exercises and examples throughout the
text making it suitable for graduate courses in the area.
This volume contains the lectures presented at the workshop on
"Advances in Mathematical Systems Theory," held on the island of
Borkum, Germany (April 20-23, 1999). The book will be of interest
to graduate students and researchers interested in control theory
and mathematical systems theory, who will find in-depth analysis
and presentations from diverse perspectives interacting in this
lively area. The editors are proud to dedicate this volume to
Diederich Hinrichsen on the occasion of his 60th birthday in
acknowl- edgment of his major contributions to linear systems
theory and control theory and his long-term achievements in
establishing mathematical sys- tems theory in Germany. We all owe
much to him as a teacher, colleague, and friend. The editors thank
the Graduiertenkolleg "Komplexe Dynamische Sys- teme" at the
University of Bremen as well as the European "Nonlinear Control
Network" for providing financial support that enabled this work-
shop. Augsburg, Germany Fritz Colonius Wiirzburg, Germany Uwe
Helmke Kaiserslautern, Germany Dieter Pratzel-Wolters Bremen,
Germany Fabian Wirth Introduction The workshop "Advances in
Mathematical Systems Theory" took place in honor of Diederich
Hinrichsen on the occasion of his 60th birthday. The following
chapters are based on invited lectures and cover a wide range of
topics in linear and nonlinear systems theory including
parameteriza- tion problems, behaviors of linear systems and
convolutional codes, as well as complementarity systems and hybrid
systems.
This volume contains the lectures presented at the workshop on
"Advances in Mathematical Systems Theory," held on the island of
Borkum, Germany (April 20-23, 1999). The book will be of interest
to graduate students and researchers interested in control theory
and mathematical systems theory, who will find in-depth analysis
and presentations from diverse perspectives interacting in this
lively area. The editors are proud to dedicate this volume to
Diederich Hinrichsen on the occasion of his 60th birthday in
acknowl- edgment of his major contributions to linear systems
theory and control theory and his long-term achievements in
establishing mathematical sys- tems theory in Germany. We all owe
much to him as a teacher, colleague, and friend. The editors thank
the Graduiertenkolleg "Komplexe Dynamische Sys- teme" at the
University of Bremen as well as the European "Nonlinear Control
Network" for providing financial support that enabled this work-
shop. Augsburg, Germany Fritz Colonius Wiirzburg, Germany Uwe
Helmke Kaiserslautern, Germany Dieter Pratzel-Wolters Bremen,
Germany Fabian Wirth Introduction The workshop "Advances in
Mathematical Systems Theory" took place in honor of Diederich
Hinrichsen on the occasion of his 60th birthday. The following
chapters are based on invited lectures and cover a wide range of
topics in linear and nonlinear systems theory including
parameteriza- tion problems, behaviors of linear systems and
convolutional codes, as well as complementarity systems and hybrid
systems.
This work is aimed at mathematics and engineering graduate students
and researchers in the areas of optimization, dynamical systems,
control sys tems, signal processing, and linear algebra. The
motivation for the results developed here arises from advanced
engineering applications and the emer gence of highly parallel
computing machines for tackling such applications. The problems
solved are those of linear algebra and linear systems the ory, and
include such topics as diagonalizing a symmetric matrix, singular
value decomposition, balanced realizations, linear programming,
sensitivity minimization, and eigenvalue assignment by feedback
control. The tools are those, not only of linear algebra and
systems theory, but also of differential geometry. The problems are
solved via dynamical sys tems implementation, either in continuous
time or discrete time, which is ideally suited to distributed
parallel processing. The problems tackled are indirectly or
directly concerned with dynamical systems themselves, so there is
feedback in that dynamical systems are used to understand and
optimize dynamical systems. One key to the new research results has
been the recent discovery of rather deep existence and uniqueness
results for the solution of certain matrix least squares
optimization problems in geomet ric invariant theory. These
problems, as well as many other optimization problems arising in
linear algebra and systems theory, do not always admit solutions
which can be found by algebraic methods."
This book contains the plenary lectures presented at the Workshop
'Operators, Systems and Linear Algebra: Three Decades of Algebraic
Systems Theory, ' held in Kaiserslautern, Germany, September 24-26,
1997. It is a Festschrift honoring the impact of the work of Paul
Fuhrmann in operator and control theory. The book includes essays
written by prominent scientists to present their views on some of
the most recent developments in the area of mathematical systems
theory and its applications. The papers cover a wide range of
theoretical and applied topics, with emphasis on computational
aspects and relations to engineering problems. The impact of Paul
Fuhrmann's work can be traced through many parts of the volume.
Polynomial models and shift realizations, the algebraic structure
of linear state feedback, partial realization theory and the
recursive inversion of Hanke! and Toeplitz operators, spectral
factorization, and parametrizations of classes of rational
functions are some of the topics in the book, where explicit
references are made to his work. It is impossible to give in this
short preface any substantial review of Paul Fuhr- mann's numerous
and major contributions to finite and infinite dimensionallinear
systems theory. Instead we like to emphasize that his work
demonstrates in a clear way the underlying attempt to unreveal the
basic unity of mathematics.
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