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The Joint Spectral Radius

Theory and Applications

  • Book
  • © 2009

Overview

Authors:
  1. Raphaël Jungers

    1. UCL/INMA, Louvain-la-Neuve, Belgium

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  • Presents most up-to-date research on the Joint Spectral Radius

Part of the book series: Lecture Notes in Control and Information Sciences (LNCIS, volume 385)

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Table of contents (11 chapters)

  1. Front Matter

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  2. Introduction

    1. Introduction

      • Raphaël Jungers
      Pages 1-3

  3. Part I Theory

    1. Front Matter

      Pages 5-5
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    2. Basics

      • Raphaël Jungers
      Pages 7-22

    3. Classical Results and Problems

      • Raphaël Jungers
      Pages 23-46

    4. Nonnegative Integer Matrices

      • Raphaël Jungers
      Pages 47-61

    5. On the Finiteness Property for Rational Matrices

      • Raphaël Jungers
      Pages 63-74

  4. Part II Applications

    1. Front Matter

      Pages 75-75
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    2. Continuity of Wavelet Functions

      • Raphaël Jungers
      Pages 77-84

    3. Capacity of Codes

      • Raphaël Jungers
      Pages 85-99

    4. Overlap-Free Words

      • Raphaël Jungers
      Pages 101-114

    5. Trackable Graphs

      • Raphaël Jungers
      Pages 115-120

    6. Conclusion

      • Raphaël Jungers
      Pages 121-123

  5. Part III Appendices

    1. Front Matter

      Pages 125-125
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    2. Appendix A Numerical Values for Overlap-Free Words

      • Raphaël Jungers
      Pages 127-131

  6. Back Matter

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Keywords

About this book

This monograph is based on the Ph.D. Thesis of the author [58]. Its goal is twofold: First, it presents most researchwork that has been done during his Ph.D., or at least the part of the work that is related with the joint spectral radius. This work was concerned with theoretical developments (part I) as well as the study of some applications (part II). As a second goal, it was the author’s feeling that a survey on the state of the art on the joint spectral radius was really missing in the literature, so that the ?rst two chapters of part I present such a survey. The other chapters mainly report personal research, except Chapter 5 which presents animportantapplicationofthejointspectralradius:thecontinuityofwavelet functions. The ?rst part of this monograph is dedicated to theoretical results. The ?rst two chapters present the above mentioned survey on the joint spectral radius. Its minimum-growth counterpart, the joint spectral subradius, is also considered. The next two chapters point out two speci?c theoretical topics, that are important in practical applications: the particular case of nonne- tive matrices, and the Finiteness Property. The second part considers applications involving the joint spectral radius.

Reviews

From the reviews:

“This very interesting and well-written monograph covers both the theory and several applications of the joint spectral radius of a set of matrices, a notion which appears in different fields of mathematics … . The monograph is made of two parts: the first addresses the theoretical aspects, while the second is focused on some applications. … I believe the book will become a standard reference for the subject.”­­­ (Nicola Guglielmi, Mathematical Reviews, Issue 2011 c)

Authors and Affiliations

  • UCL/INMA, Louvain-la-Neuve, Belgium

    Raphaël Jungers

Bibliographic Information

  • Book Title: The Joint Spectral Radius

  • Book Subtitle: Theory and Applications

  • Authors: Raphaël Jungers

  • Series Title: Lecture Notes in Control and Information Sciences

  • DOI: https://doi.org/10.1007/978-3-540-95980-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2009

  • Softcover ISBN: 978-3-540-95979-3Published: 19 May 2009

  • eBook ISBN: 978-3-540-95980-9Published: 15 May 2009

  • Series ISSN: 0170-8643

  • Series E-ISSN: 1610-7411

  • Edition Number: 1

  • Number of Pages: XIV, 146

  • Number of Illustrations: 18 b/w illustrations

  • Topics: Control, Robotics, Mechatronics, Systems Theory, Control

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