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Delay Systems pp 31–44Cite as

New Integral Inequality and Its Application to Time-Delay Systems

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Part of the book series: Advances in Delays and Dynamics ((ADVSDD,volume 1))

Abstract

In the last decade, the Jensen’s inequality has been intensively used in the context of time-delay or sampled-data systems since it is an appropriate tool to obtain tractable stability conditions expressed in terms linear matrix inequalities (LMI). However, it is also well-known that this inequality unavoidably introduces an undesirable conservatism in the stability conditions and looking at the literature, reducing this gap is still an open problem. In this paper, we propose an alternative inequality based on the Fourier Theory, more precisely on the Wirtinger’s inequalities. It is showed in this chapter that they allow deriving a new integral inequality which is proved to encompass the Jensen’s inequality. In order to illustrate the potential gain of employing this new inequality with respect to the Jensen’s one, an application to time-delay analysis is provided.

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Author information

Authors and Affiliations

  1. CNRS, LAAS, 7 avenue du Colonel Roche, 31077, Toulouse, France

    Alexandre Seuret & Frédéric Gouaisbaut

  2. Univ de Toulouse, LAAS, F-31400, Toulouse, France

    Alexandre Seuret

  3. Univ de Toulouse, UPS, LAAS, F-31400, Toulouse, France

    Frédéric Gouaisbaut

Authors
  1. Alexandre Seuret
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  2. Frédéric Gouaisbaut
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Corresponding author

Correspondence to Alexandre Seuret .

Editor information

Editors and Affiliations

  1. Dept. of Instrumentation & Control Eng. Faculty of Mechanical Engineering, Czech Technical University, Prague, Czech Republic

    Tomáš Vyhlídal

  2. Institut de Recherche en Communications et Cybernétique de Nantes, Nantes Cedex 3, France

    Jean-François Lafay

  3. Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts, USA

    Rifat Sipahi

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Seuret, A., Gouaisbaut, F. (2014). New Integral Inequality and Its Application to Time-Delay Systems. In: Vyhlídal, T., Lafay, JF., Sipahi, R. (eds) Delay Systems. Advances in Delays and Dynamics, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-01695-5_3

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  • DOI: https://doi.org/10.1007/978-3-319-01695-5_3

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-01694-8

  • Online ISBN: 978-3-319-01695-5

  • eBook Packages: EngineeringEngineering (R0)

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