One of the main problems in control theory is the stabilization
problem consisting of finding a feedback control law ensuring
stability; when the linear approximation is considered, the nat
ural problem is stabilization of a linear system by linear state
feedback or by using a linear dynamic controller. This prob lem was
intensively studied during the last decades and many important
results have been obtained. The present monograph is based mainly
on results obtained by the authors. It focuses on stabilization of
systems with slow and fast motions, on stabilization procedures
that use only poor information about the system (high-gain
stabilization and adaptive stabilization), and also on discrete
time implementa tion of the stabilizing procedures. These topics
are important in many applications of stabilization theory. We hope
that this monograph may illustrate the way in which mathematical
theories do influence advanced technol ogy. This book is not
intended to be a text book nor a guide for control-designers. In
engineering practice, control-design is a very complex task in
which stability is only one of the re quirements and many aspects
and facets of the problem have to be taken into consideration. Even
if we restrict ourselves to stabilization, the book does not
provide just recipes, but it fo cuses more on the ideas lying
behind the recipes. In short, this is not a book on control, but on
some mathematics of control."
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