Admissibility of control operators for positive semigroups and robustness of input-to-state stability
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.
Keywords
Cite
@article{arxiv.2503.04097,
title = {Admissibility of control operators for positive semigroups and robustness of input-to-state stability},
author = {Yassine El Gantouh and Yang Liu and Jianquan Lu and Jinde Cao},
journal= {arXiv preprint arXiv:2503.04097},
year = {2026}
}