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

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Delays and Interconnections: Methodology, Algorithms and Applications

Part of the book series: Advances in Delays and Dynamics ((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.

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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.

Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Northeastern University, Shenyang, 110819, Liaoning, China

    Xu-Guang Li & Lu Zhang

  2. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110819, Liaoning, China

    Xu-Guang Li & Lu Zhang

  3. Laboratoire des Signaux et Systèmes (L2S UMR CNRS 8506), CNRS-CentraleSupélec-Université Paris-Sud, 91192, Gif-Sur-Yvette, France

    Silviu-Iulian Niculescu

  4. UPE, ESIEE Paris, Laboratoire Images, Signaux et Systèmes Intelligents, 93162, Noisy-Le-Grand, France

    Arben Çela

Authors
  1. Xu-Guang Li
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  2. Silviu-Iulian Niculescu
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  3. Arben Çela
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  4. Lu Zhang
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Corresponding author

Correspondence to Xu-Guang Li .

Editor information

Editors and Affiliations

  1. Laboratoire des Signaux et Systèmes, CNRS-CentraleSupèlec-Université Paris-Saclay, Gif-sur-Yvette, France

    Giorgio Valmorbida

  2. Laboratoire d’Analyse et d’Architecture de Systèmes-CNRS, Toulouse, France

    Alexandre Seuret

  3. Laboratoire des Signaux et Systèmes, CNRS-CentraleSupèlec-Université Paris-Saclay, Gif-sur-Yvette, France

    Islam Boussaada

  4. Mechanical and Industrial Engineering, Northeastern University, Boston, MA, USA

    Rifat Sipahi

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Li, XG., Niculescu, SI., Çela, A., Zhang, L. (2019). Stability Analysis of Uniformly Distributed Delay Systems: A Frequency-Sweeping Approach. In: Valmorbida, G., Seuret, A., Boussaada, I., Sipahi, R. (eds) Delays and Interconnections: Methodology, Algorithms and Applications. Advances in Delays and Dynamics, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-030-11554-8_8

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