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Lyapunov Functionals and Matrices for Neutral Type 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

In this chapter we present some basic results concerning the computation of quadratic functionals with prescribed time derivatives for linear neutral type time delay systems. The functionals are defined by special matrix valued functions. These functions are called Lyapunov matrices. Basic results with respect to the existence and uniqueness of the matrices are included. Some important applications of the functionals and matrices are pointed out. A brief historical survey ends the chapter.

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Authors and Affiliations

  1. Faculty of Applied Mathematics and Control Processes, St.-Petersburg State University, St.-Petersburg, 198504, Russia

    Vladimir L. Kharitonov

Authors
  1. Vladimir L. Kharitonov
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Correspondence to Vladimir L. Kharitonov .

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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Kharitonov, V.L. (2012). Lyapunov Functionals and Matrices for Neutral Type 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_1

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  • DOI: https://doi.org/10.1007/978-3-642-25221-1_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25220-4

  • Online ISBN: 978-3-642-25221-1

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