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Stability Analysis of Uniformly Distributed Delay Systems: A Frequency-Sweeping Approach

  • Xu-Guang LiEmail author
  • Silviu-Iulian Niculescu
  • Arben Çela
  • Lu Zhang
Chapter
Part of the Advances in Delays and Dynamics book series (ADVSDD, volume 10)

Abstract

This chapter addresses the stability of a class of systems including uniformly distributed delays. Compared with the existing results for systems with point-wise constant delays, this problem involves three new technical issues. In this chapter, these technical issues will be solved mainly within the frequency-sweeping framework which was recently established for systems with point-wise delays. As a consequence, the stability in the whole domain of delay can be studied. Moreover, a unified approach will be proposed: Most of the steps required by the problem can be fulfilled by simply observing the frequency-sweeping curves.

Notes

Acknowledgements

X.-G. Li is supported by National Natural Science Foundation of China (61473065), Fundamental Research Funds for the Central Universities (N160402001), and “Digiteo invites” program of France.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Xu-Guang Li
    • 1
    • 2
    Email author
  • Silviu-Iulian Niculescu
    • 3
  • Arben Çela
    • 4
  • Lu Zhang
    • 1
    • 2
  1. 1.School of Information Science and EngineeringNortheastern UniversityShenyangChina
  2. 2.State Key Laboratory of Synthetical Automation for Process IndustriesNortheastern UniversityShenyangChina
  3. 3.Laboratoire des Signaux et Systèmes (L2S UMR CNRS 8506), CNRS-CentraleSupélec-Université Paris-SudGif-Sur-YvetteFrance
  4. 4.UPE, ESIEE Paris, Laboratoire Images, Signaux et Systèmes IntelligentsNoisy-Le-GrandFrance

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