Hankel norm approximation for infinite-dimensional systems

A. Sasane

Model reduction is an important engineering problem in which one aims to replace an elaborate model by a simpler model without undue loss of accuracy. The accuracy can be mathematically measured in several possible norms and the Hankel norm is one such. The Hankel norm gives a meaningful notion of distance between two linear systems: roughly speaking, it is the induced norm of the operator that maps past inputs to future outputs. It turns out that the engineering problem of model reduction in the Hankel norm is closely related to the mathematical problem of finding solutions to the sub-optimal Nehari-Takagi problem, which is called "the sub-optimal Hankel norm approximation problem" in this book. Although the existence of a solution to the sub-optimal Hankel norm approximation problem has been known since the 1970's, this book presents explicit solutions and, in particular, new formulae for several large classes of infinite-dimensional systems for the first time.

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  • Classes of well-posed linear systems.- Compactness and nuclearity of Hankel operators.- Characterization of all solutions.- State space solutions.- The non-exponentially stable case.- The case of regular linear systems.- Coda.

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書名 Hankel norm approximation for infinite-dimensional systems
著作者等 Sasane A.
Sasane Amol
シリーズ名 Engineering online library
Lecture notes in control and information sciences
出版元 Springer
刊行年月 c2002
ページ数 viii, 142 p.
大きさ 24 cm
ISBN 3540433279
NCID BA57200149
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言語 英語
出版国 ドイツ