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Sufficient Stability Conditions for Time-varying Networks of Telegrapher's Equations or Difference Delay Equations

Abstract : We give a sufficient condition for exponential stability of a network of lossless telegrapher's equations, coupled by linear time-varying boundary conditions. The sufficient conditions is in terms of dissipativity of the couplings, which is natural for instance in the context of microwave circuits. Exponential stability is with respect to any $L^p$-norm, $1\leq p\leq\infty$. This also yields a sufficient condition for exponential stability to a special class of linear time-varying difference delay systems which is quite explicit and tractable. One ingredient of the proof is that $L^p$ exponential stability for such difference delay systems is independent of $p$, thereby reproving in a simpler way some results from [3].
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https://hal.inria.fr/hal-02385548
Contributor : Jean-Baptiste Pomet <>
Submitted on : Thursday, November 28, 2019 - 7:48:44 PM
Last modification on : Tuesday, May 26, 2020 - 6:50:59 PM
Document(s) archivé(s) le : Saturday, February 29, 2020 - 8:00:08 PM

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  • HAL Id : hal-02385548, version 1
  • ARXIV : 1911.13003

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Laurent Baratchart, Sébastien Fueyo, Gilles Lebeau, Jean-Baptiste Pomet. Sufficient Stability Conditions for Time-varying Networks of Telegrapher's Equations or Difference Delay Equations. 2019. ⟨hal-02385548⟩

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