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arXiv · 2606.23549

Exponential stability of abstract boundary-coupled positive systems

Yassine El Gantouh·Mahyar Mahinzaeim
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Abstract

In this paper, we study the well-posedness and exponential stability of a class of abstract boundary-coupled positive systems. Within a general semigroup framework, we establish well-posedness in terms of existence, uniqueness, and regularity of solutions. More concretely, we derive some simple and readily verifiable tests on the boundary coupling operators for the verification of the well-posedness of the coupled system and, at the same time, provide spectral criteria that guarantee exponential stability of the solutions. The analysis is based on two complementary approaches: the feedback-theoretic method and perturbation techniques for resolvent positive operators on Banach lattices (i.e., Banach spaces equipped with a compatible order structure). This unified framework allows for a systematic treatment of a broad class of boundary couplings in abstract dynamical systems. Several examples are presented to illustrate the applicability of the theoretical results.

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Yassine El Gantouh, Mahyar Mahinzaeim. 2026-06-22. Exponential stability of abstract boundary-coupled positive systems. https://arxiv.org/abs/2606.23549

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