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Hankel Norm Approximation for Infinite-Dimensional Systems

  • Amol┬áSasane

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 277)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Pages 1-12
  3. Pages 101-108
  4. Pages 127-129
  5. Back Matter
    Pages 131-142

About this book

Introduction

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 1970s, this book presents explicit solutions and, in particular, new formulae for several large classes of infinite-dimensional systems for the first time.

Keywords

Mathematica distance model operator

Authors and affiliations

  • Amol┬áSasane
    • 1
  1. 1.Signals, Systems and Control Dept. Faculty of Mathematical SciencesUniversity of TwenteEnschedeThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-45877-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-43327-9
  • Online ISBN 978-3-540-45877-7
  • Series Print ISSN 0170-8643
  • Buy this book on publisher's site
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