Sufficient Stability Conditions for Time-varying Networks of Telegrapher's Equations or Difference Delay Equations
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| Main Authors: | , , , |
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| Format: | Preprint |
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2019
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| _version_ | 1866914963649462272 |
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| author | Baratchart, Laurent Fueyo, Sébastien Lebeau, Gilles Pomet, Jean-Baptiste |
| author_facet | Baratchart, Laurent Fueyo, Sébastien Lebeau, Gilles Pomet, Jean-Baptiste |
| contents | 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 [Y. Chitour, G. Mazanti, and M. Sigalotti, $\it {Netw. Heterog. Media}$, 11 (2016), pp. 563--601]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1911_13003 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Sufficient Stability Conditions for Time-varying Networks of Telegrapher's Equations or Difference Delay Equations Baratchart, Laurent Fueyo, Sébastien Lebeau, Gilles Pomet, Jean-Baptiste Dynamical Systems Optimization and Control 37L15, 39A30, 35L51, 35L65 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 [Y. Chitour, G. Mazanti, and M. Sigalotti, $\it {Netw. Heterog. Media}$, 11 (2016), pp. 563--601]. |
| title | Sufficient Stability Conditions for Time-varying Networks of Telegrapher's Equations or Difference Delay Equations |
| topic | Dynamical Systems Optimization and Control 37L15, 39A30, 35L51, 35L65 |
| url | https://arxiv.org/abs/1911.13003 |