Analytic Curve Frequency-Sweeping Stability Tests for Systems with Commensurate Delays

  • Xu-Guang Li
  • Silviu-Iulian Niculescu
  • Arben Cela

Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)

Also part of the SpringerBriefs in Control, Automation and Robotics book sub series (BRIEFSCONTROL)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Xu-Guang Li, Silviu-Iulian Niculescu, Arben Çela
    Pages 1-16
  3. Xu-Guang Li, Silviu-Iulian Niculescu, Arben Çela
    Pages 17-26
  4. Xu-Guang Li, Silviu-Iulian Niculescu, Arben Çela
    Pages 27-34
  5. Xu-Guang Li, Silviu-Iulian Niculescu, Arben Çela
    Pages 35-46
  6. Xu-Guang Li, Silviu-Iulian Niculescu, Arben Çela
    Pages 47-52
  7. Xu-Guang Li, Silviu-Iulian Niculescu, Arben Çela
    Pages 53-62
  8. Xu-Guang Li, Silviu-Iulian Niculescu, Arben Çela
    Pages 63-72
  9. Xu-Guang Li, Silviu-Iulian Niculescu, Arben Çela
    Pages 73-80
  10. Xu-Guang Li, Silviu-Iulian Niculescu, Arben Çela
    Pages 81-89
  11. Xu-Guang Li, Silviu-Iulian Niculescu, Arben Çela
    Pages 91-104
  12. Xu-Guang Li, Silviu-Iulian Niculescu, Arben Çela
    Pages 105-108
  13. Back Matter
    Pages 109-130

About this book

Introduction

In this brief the authors establish a new frequency-sweeping framework to solve the complete stability problem for time-delay systems with commensurate delays. The text describes an analytic curve perspective which allows a deeper understanding of spectral properties focusing on the asymptotic behavior of the characteristic roots located on the imaginary axis as well as on properties invariant with respect to the delay parameters. This asymptotic behavior is shown to be related by another novel concept, the dual Puiseux series which helps make frequency-sweeping curves useful in the study of general time-delay systems. The comparison of Puiseux and dual Puiseux series leads to three important results:

  • an explicit function of the number of unstable roots simplifying analysis and design of time-delay systems so that to some degree they may be dealt with as finite-dimensional systems;
  • categorization of all time-delay systems into three types according to their ultimate stability properties; and
  • a simple frequency-sweeping criterion allowing asymptotic behavior analysis of critical imaginary roots for all positive critical delays by observation.

Academic researchers and graduate students interested in time-delay systems and practitioners working in a variety of fields – engineering, economics and the life sciences involving transfer of materials, energy or information which are inherently non-instantaneous, will find the results presented here useful in tackling some of the complicated problems posed by delays.

Keywords

Analytic Curves Asymptotic Behvior Frequency-domain Approach Frequency-sweeping Curves Puiseux Series Time Delay Systems

Authors and affiliations

  • Xu-Guang Li
    • 1
  • Silviu-Iulian Niculescu
    • 2
  • Arben Cela
    • 3
  1. 1.School of Information Science and EngineeringNortheastern UniversityShenyangChina
  2. 2.Laboratoire des Signaux et Systèmes (L2S, UMR CNRS 8506)CNRS - Centrale Supélec-Université Paris-SudGif-sur-YvetteFrance
  3. 3.Department of Computer Science and TelecommunicationUniversité Paris-EstNoisy-le-GrandFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-15717-7
  • Copyright Information The Author(s) 2015
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-15716-0
  • Online ISBN 978-3-319-15717-7
  • Series Print ISSN 2191-8112
  • Series Online ISSN 2191-8120
  • About this book
Industry Sectors
Automotive
Chemical Manufacturing
Electronics
Energy, Utilities & Environment
Aerospace
Oil, Gas & Geosciences
Engineering