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Hankel Norm Approximation for Infinite-Dimensional Systems

  • Book
  • © 2002

Overview

Authors:
  1. Amol Sasane

    1. Signals, Systems and Control Dept. Faculty of Mathematical Sciences, University of Twente, Enschede, The Netherlands

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  • Explicit solutions to the sub-optimal Hankel norm approximation problem are presented for the first time
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Introduction

    Pages 1-12

  3. Classes of well-posed linear systems

    Pages 13-62

  4. Compactness and nuclearity of Hankel operators

    Pages 63-83

  5. Characterization of all solutions

    Pages 85-99

  6. State space solutions

    Pages 101-108

  7. The non-exponentially stable case

    Pages 109-117

  8. The case of regular linear systems

    Pages 119-125

  9. Coda

    Pages 127-129

  10. Back Matter

    Pages 131-142
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Keywords

About this book

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.

Authors and Affiliations

  • Signals, Systems and Control Dept. Faculty of Mathematical Sciences, University of Twente, Enschede, The Netherlands

    Amol Sasane

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