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Time Delay Systems: Methods, Applications and New Trends pp 19–33Cite as

On the Stability of Positive Difference Equations

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

Abstract

In this chapter, we are interested with stability of linear continuous-time difference equations. These equations involve delays, which can be non commensurable. Spectrum analysis comes down to the zeros analysis of an exponential polynomial. From previous results on stability dependent or independent of delays, we focus on the particular case of positive difference equations. It is proved that the stability of linear difference equations with positive coefficients is robust with respect to variations of the delays, and are given exponential bounds for the solution.

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Author information

Authors and Affiliations

  1. AMPERE, UMR CNRS 5005, INSA-Lyon, Avenue Jean Capelle, 69621, Villeurbanne Cedex, France

    Michael Di Loreto

  2. Institut de Recherche en Communications et Cyberntique de Nantes (IRCCyN), UMR CNRS 6597, Ecole Centrale de Nantes, BP 92101, 44321, Nantes Cedex 03, France

    Jean Jacques Loiseau

Authors
  1. Michael Di Loreto
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  2. Jean Jacques Loiseau
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Corresponding author

Correspondence to Michael Di Loreto .

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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Di Loreto, M., Loiseau, J.J. (2012). On the Stability of Positive Difference Equations. 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_2

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  • DOI: https://doi.org/10.1007/978-3-642-25221-1_2

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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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