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This self-contained monograph describes basic set-theoretic methods
for control. It provides a discussion of their links to fundamental
problems in Lyapunov stability analysis and stabilization, optimal
control, control under constraints, persistent disturbance
rejection, and uncertain systems analysis and synthesis. The work
presents several established and potentially new applications,
along with numerical examples and case studies. A key theme is the
trade-off between exact (but computationally intensive) and
approximate (but conservative) solutions to problems. Mathematical
language is kept to the minimum necessary.
The second edition of this monograph describes the set-theoretic
approach for the control and analysis of dynamic systems, both from
a theoretical and practical standpoint. This approach is linked to
fundamental control problems, such as Lyapunov stability analysis
and stabilization, optimal control, control under constraints,
persistent disturbance rejection, and uncertain systems analysis
and synthesis. Completely self-contained, this book provides a
solid foundation of mathematical techniques and applications,
extensive references to the relevant literature, and numerous
avenues for further theoretical study. All the material from the
first edition has been updated to reflect the most recent
developments in the field, and a new chapter on switching systems
has been added. Each chapter contains examples, case studies, and
exercises to allow for a better understanding of theoretical
concepts by practical application. The mathematical language is
kept to the minimum level necessary for the adequate formulation
and statement of the main concepts, yet allowing for a detailed
exposition of the numerical algorithms for the solution of the
proposed problems. Set-Theoretic Methods in Control will appeal to
both researchers and practitioners in control engineering and
applied mathematics. It is also well-suited as a textbook for
graduate students in these areas. Praise for the First Edition
"This is an excellent book, full of new ideas and collecting a lot
of diverse material related to set-theoretic methods. It can be
recommended to a wide control community audience." - B. T. Polyak,
Mathematical Reviews "This book is an outstanding monograph of a
recent research trend in control. It reflects the vast experience
of the authors as well as their noticeable contributions to the
development of this field...[It] is highly recommended to PhD
students and researchers working in control engineering or applied
mathematics. The material can also be used for graduate courses in
these areas." - Octavian Pastravanu, Zentralblatt MATH
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