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arXiv · 2503.04097

Admissibility of control operators for positive semigroups and robustness of input-to-state stability

Yassine El Gantouh·Yang Liu·Jianquan Lu·Jinde Cao
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Abstract

In this paper, we investigate well-posedness and stability properties of distributed parameter systems, with particular emphasis on linear positive control systems. We establish a characterization of the well-posedness in the Banach lattice setting. Furthermore, we derive a resolvent condition for admissibility of control operators for positive semigroups. In addition, we study the behavior of input-to-state stability (ISS) under unbounded perturbations of the underlying semigroup generator. More precisely, we establish necessary and sufficient conditions for the robustness of ISS under Desch-Schappacher perturbations. Our theoretical results are demonstrated through a boundary value-controlled transport equation with non-local boundary conditions.

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Yassine El Gantouh, Yang Liu, Jianquan Lu, Jinde Cao. 2025-03-06. Admissibility of control operators for positive semigroups and robustness of input-to-state stability. https://arxiv.org/abs/2503.04097

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