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Analytic curve frequency-sweeping stability tests for systems with commensurate delays [electronic resource] / Xu-Guang Li, Silviu-Iulian Niculescu, Arben Çela.

Li, Xu-Guang, author.; Niculescu, Silviu-Iulian, author.; Çela, Arben, author.
2015
TJ216
Available Online
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Title
Analytic curve frequency-sweeping stability tests for systems with commensurate delays [electronic resource] / Xu-Guang Li, Silviu-Iulian Niculescu, Arben Çela.
Author
Li, Xu-Guang, author.
ISBN
9783319157177 electronic book
3319157175 electronic book
9783319157160
DOI
https://doi.org/10.1007/978-3-319-15717-7
Published
Cham : Springer, [2015]
Language
English
Description
1 online resource : illustrations.
Item Number
10.1007/978-3-319-15717-7 doi
Call Number
TJ216
Dewey Decimal Classification
629.8
Summary
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 {u2013} 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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (viewed April 13, 2015).
Added Author
Niculescu, Silviu-Iulian, author.
Çela, Arben, author.
Series
SpringerBriefs in electrical and computer engineering. Control, automation and robotics.
Available in Other Form
Print version: 9783319157160
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All Resources
Introduction to the Stability of Time-Delay Systems
Introduction to Analytic Curves
Analytic Curve Perspective for Time-Delay Systems
Computing Puiseux Series for a Critical Pair
Invariance Property: A Unique Idea for Complete Stability Analysis
Invariance Property for Critical Imaginary Roots (CIRs) with Index g = 1
Invariance Property for Critical Imaginary Roots with Index n = 1
Invariance Conjecture and Frequency-Sweeping Framework
Complex Stability for Time-Delay Systems: A Unified Approach
Extension to Neutral Time-Delay Systems
Concluding Remarks and Further Perspectives.

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