A Spectral-based ISS small-gain theorem for boundary control systems with infinite couplings
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866917402118193152 |
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| author | Gantouh, Yassine El Zheng, Jun Zhu, Guchuan Li, Dingshi |
| author_facet | Gantouh, Yassine El Zheng, Jun Zhu, Guchuan Li, Dingshi |
| contents | We study the input-to-state stability (ISS) of boundary control systems allowing for infinitely many boundary couplings. Using semigroup perturbation theory and the theory of positive linear operators on Banach lattices, we derive a spectral small-gain condition ensuring exponential ISS. We further investigate linear Boltzmann-type equations on an infinite network of intersecting circles, incorporating delays, scattering, and disturbances acting at the junction. For this class of systems, we prove that a spectral small-gain condition on the transmission operator matrix guarantees exponential ISS with respect to disturbances propagating through the network. Moreover, we derive explicit ISS estimates for {certain} classes of dynamical processes. Finally, we demonstrate the practical applicability of our results by considering two important classes of time-delayed transmission conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11031 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Spectral-based ISS small-gain theorem for boundary control systems with infinite couplings Gantouh, Yassine El Zheng, Jun Zhu, Guchuan Li, Dingshi Optimization and Control We study the input-to-state stability (ISS) of boundary control systems allowing for infinitely many boundary couplings. Using semigroup perturbation theory and the theory of positive linear operators on Banach lattices, we derive a spectral small-gain condition ensuring exponential ISS. We further investigate linear Boltzmann-type equations on an infinite network of intersecting circles, incorporating delays, scattering, and disturbances acting at the junction. For this class of systems, we prove that a spectral small-gain condition on the transmission operator matrix guarantees exponential ISS with respect to disturbances propagating through the network. Moreover, we derive explicit ISS estimates for {certain} classes of dynamical processes. Finally, we demonstrate the practical applicability of our results by considering two important classes of time-delayed transmission conditions. |
| title | A Spectral-based ISS small-gain theorem for boundary control systems with infinite couplings |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.11031 |