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Observation and Control for Operator Semigroups (Hardcover, 2009 ed.)
Loot Price: R2,986
Discovery Miles 29 860
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Observation and Control for Operator Semigroups (Hardcover, 2009 ed.)
Series: Birkhauser Advanced Texts / Basler Lehrbucher
Expected to ship within 10 - 15 working days
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The evolution of the state of many systems modeled by linear
partial di?erential equations (PDEs) or linear delay di?erential
equations can be described by ope- torsemigroups.Thestate ofsucha
systemis anelementin anin?nite-dimensional normed space, whence the
name "in?nite-dimensional linear system". The study of operator
semigroups is a mature area of functional analysis, which is still
very active. The study of observation and control operators for
such semigroups is relatively more recent. These operators are
needed to model the - teraction of a system with the surrounding
world via outputs or inputs. The main
topicsofinterestaboutobservationandcontroloperatorsareadmissibility,obse-
ability, controllability, stabilizability and detectability.
Observation and control operators are an essential ingredient of
well-posed linear systems (or more gen- ally system nodes). In this
book we deal only with admissibility, observability and
controllability. We deal only with operator semigroups acting on
Hilbert spaces. This book is meant to be an elementary introduction
into the topics m- tioned above. By "elementary" we mean that we
assume no prior knowledge of ?nite-dimensional control theory, and
no prior knowledge of operator semigroups or of unbounded
operators. We introduce everything needed from these areas. We do
assume that the reader has a basic understanding of bounded
operators on Hilbert spaces, di?erential equations, Fourier and
Laplace transforms, dist- butions and Sobolev spaces on
n-dimensional domains. Much of the background needed in these areas
is summarized in the appendices, often with proofs.
General
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