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Positivity of Complete Quadratic Lyapunov-Krasovskii Functionals in Time-Delay Systems

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Time Delay Systems: Methods, Applications and New Trends

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 423))

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Abstract

This chapter discusses positivity of quadratic functionals that arise in the stability analysis of time-delay systems. When both the single and double integral terms are positive, a necessary and sufficient condition for positivity is obtained using operator theory. This is applied to the Lyapunov-Krasovskii functional and its derivative. The coupled differential-difference equations are studied using the Sum-of-Squares (SOS) method.

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Author information

Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, Illinois, 62026, USA

    Keqin Gu

  2. School of Automation, Nanjing University of Science and Technology, Nanjing, China

    Yashun Zhang

  3. Department of Mechanical, Materials, and Aerospace Engineering, Illinois Institute of Technology, Chicago, Illinois, 60616, USA

    Matthew Peet

Authors
  1. Keqin Gu
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  2. Yashun Zhang
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  3. Matthew Peet
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Corresponding author

Correspondence to Keqin Gu .

Editor information

Editors and Affiliations

  1. Dept. Mechanical Engineering, Northeastern University, Huntingdon Ave. 360, Boston, 02115, Massachusetts, USA

    Rifat Sipahi

  2. Technicka Street 4, Prague, 166 07, Czech Republic

    Tomáš Vyhlídal

  3. , CNRSSupélec, L2S (UMR CNRS 8506), rue Joliot Curie 3, Gif-sur-Yvette, 91192, France

    Silviu-Iulian Niculescu

  4. , Department of Electrical and Information, University of L’Aquila, Via G. Gronchi 18, L’Aquila, 67100, Italy

    Pierdomenico Pepe

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© 2012 Springer-Verlag GmbH Berlin Heidelberg

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Gu, K., Zhang, Y., Peet, M. (2012). Positivity of Complete Quadratic Lyapunov-Krasovskii Functionals in Time-Delay Systems. In: Sipahi, R., Vyhlídal, T., Niculescu, SI., Pepe, P. (eds) Time Delay Systems: Methods, Applications and New Trends. Lecture Notes in Control and Information Sciences, vol 423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25221-1_3

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  • DOI: https://doi.org/10.1007/978-3-642-25221-1_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25220-4

  • Online ISBN: 978-3-642-25221-1

  • eBook Packages: EngineeringEngineering (R0)

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