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A Numerical Method for the Construction of Lyapunov Matrices for Linear Periodic Systems with Time Delay

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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))

Abstract

A numerical procedure for the construction of Lyapunov matrices is proposed. It is shown that the matrices satisfy an auxiliary two-point boundary value problem for a special delay free system of matrix equations. Some applications of the functionals are also given. In this paper we study the problem of computation of Lyapunov functionals with a prescribed time derivative for the case of delay systems with periodic coefficients. Similar to the case of time invariant systems the functionals are defined by special Lyapunov matrices.

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Authors and Affiliations

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

    Olga N. Letyagina & Alexey P. Zhabko

Authors
  1. Olga N. Letyagina
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  2. Alexey P. Zhabko
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Corresponding author

Correspondence to Olga N. Letyagina .

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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Letyagina, O.N., Zhabko, A.P. (2012). A Numerical Method for the Construction of Lyapunov Matrices for Linear Periodic Systems with Time Delay. 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_20

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  • DOI: https://doi.org/10.1007/978-3-642-25221-1_20

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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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