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Software for Stability and Bifurcation Analysis of Delay Differential Equations and Applications to Stabilization

  • Conference paper
Advances in Time-Delay Systems

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 38))

Abstract

DDE-BIFTOOL is a Matlab software package for the stability and bifurcation analysis of parameter-dependent systems of delay differential equations. Using continuation, branches of steady state solutions and periodic solutions can be computed. The local stability of a solution is determined by computing relevant eigenvalues (steady state solutions) or Floquet Multipliers (periodic solutions). Along branches of solutions, bifurcations can be detected and branches of fold or Hopf bifurcation points can be computcd. We outline the capabilities of the package and some of the numerical methods upon which it is based. We illustrate the usage of the package for the analysis of two model problems and we outline applications and extensions towards controller synthesis problems. We explain how its stability routines can be used for the implementation of the continuous pole placement method, which allows to solve stabilization problems where multiple parameters need to be tuned simultaneously.

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Author information

Authors and Affiliations

  1. Department of Computer Science, K.U. Leuven, Celestijnenlaan 200A, 3001, Heverlee, Belgium

    Dirk Roose, Tatyana Luzyanina, Koen Engelborghs & Wim Michiels

Authors
  1. Dirk Roose
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  2. Tatyana Luzyanina
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  3. Koen Engelborghs
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  4. Wim Michiels
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Editor information

Editors and Affiliations

  1. Centre de Recherche de Royallieu, Universite de Technologie de Compiègne, UMR CNRS 6022, 60205, Compiègne, France

    Silviu-Iulian Niculescu

  2. Department of Mechanical and Industrial Engineering, Southern Illinois University, Edwardsville, IL, 62025-1805, USA

    Keqin Gu

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© 2004 Springer-Verlag Berlin Heidelberg

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Roose, D., Luzyanina, T., Engelborghs, K., Michiels, W. (2004). Software for Stability and Bifurcation Analysis of Delay Differential Equations and Applications to Stabilization. In: Niculescu, SI., Gu, K. (eds) Advances in Time-Delay Systems. Lecture Notes in Computational Science and Engineering, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18482-6_12

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  • DOI: https://doi.org/10.1007/978-3-642-18482-6_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20890-7

  • Online ISBN: 978-3-642-18482-6

  • eBook Packages: Springer Book Archive

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