Singular Perturbation Approach for Linear Coupled ODE-PDE Systems

  • Ying Tang
  • Christophe Prieur
  • Antoine GirardEmail author
Part of the Advances in Delays and Dynamics book series (ADVSDD, volume 10)


This paper focuses on a class of linear coupled ODE-PDE systems whose dynamics evolve in two time scales. The fast time scale modeled by a small positive perturbation parameter is introduced to the dynamics either of the ODE or of the PDE. By setting the perturbation parameter to zero, two subsystems, namely the reduced and the boundary-layer subsystems, are formally computed. Firstly, we propose a sufficient stability condition for the full coupled system. This stability condition implies the stability of both subsystems. Then, we state an approximation of the full coupled ODE-PDE systems by the subsystems based on the singular perturbation method. The error between the solution of the full system and that of the subsystems is the order of the perturbation parameter. Finally, numerical simulations on academic examples illustrate the theoretical results.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Université de Lorraine, CRAN UMR 7039 and CNRSVandoeuvre-lès-NancyFrance
  2. 2.GIPSA-labSaint Martin d’Hères CedexFrance
  3. 3.Laboratoire des signaux et systèmes (L2S)CNRS, CentraleSupélec, Université Paris-Sud, Université Paris-SaclayGif-sur-Yvette CedexFrance

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