Spectral Analysis of a Class of Linear Hyperbolic Partial Differential Equations

Anthony Hastir, Birgit Jacob, Hans Zwart

Research output: Contribution to journalArticleAcademicpeer-review


A class of linear hyperbolic partial differential equations, sometimes called networks of waves, is considered. For this class of systems, necessary and sufficient conditions are formulated on the system matrices for the operator dynamics to be a Riesz-spectral operator. In that case, its spectrum is computed explicitly, together with the corresponding eigenfunctions, which constitutes the main result of our note. In particular, this enables to characterize easily many different concepts, such as stability. We apply our results to characterize exponential stability of a co-current heat exchanger.

Original languageEnglish
Number of pages6
JournalIEEE Control Systems Letters
Publication statusE-pub ahead of print/First online - 20 May 2024


  • 2024 OA procedure
  • Discrete Riesz-spectral operators
  • Distributed parameter systems
  • Eigenvalues and eigenfunctions
  • Generators
  • Hyperbolic partial differential equations
  • Mathematical models
  • Partial differential equations
  • Spectral analysis
  • Stability criteria
  • Stability of linear systems
  • Boundary conditions


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