@article{fa781d0c33b24b1cbfa8fad1b4cadc95,
title = "Locally positive stabilization of infinite-dimensional linear systems by state feedback",
abstract = "An overview is given of the locally positive stabilization problem for positive infinite-dimensional linear systems with a bounded control operator. The impossibility of solving this problem by using a nonnegative input is established. Two methods for solving the problem by means of state feedback, namely spectral decomposition and control invariance, are described. The results are illustrated by means of a perturbed diffusion equation with Dirichlet boundary conditions and a diffusion equation with Neumann boundary conditions and pointwise control.",
keywords = "Distributed parameter systems, Partial differential equations, Positive infinite-dimensional systems, Set invariance, Stabilization, State feedback",
author = "B. Abouza{\"i}d and Achhab, {M. E.} and Dehaye, {J. N.} and A. Hastir and Winkin, {J. J.}",
note = "Funding Information: The authors wish to thank Abdelmoumen Noureddine (University Chaoua{\"i} b Doukkali, El Jadida, Morocco) for having performed numerical simulations for the example of Subsection 5.1. This research was partly conducted with the financial support of F.R.S-FNRS. Anthony Hastir is a FNRS Research Fellow under the grant FC 29535. This paper is dedicated to the memory of J. Winkin's mother Juliette Schul. The authors also wish to dedicate this paper to the memory of Pr. Ruth Curtain for her numerous contributions in infinite-dimensional systems theory. Publisher Copyright: {\textcopyright} 2021 European Control Association",
year = "2022",
month = jan,
doi = "10.1016/j.ejcon.2021.07.006",
language = "English",
volume = "63",
pages = "1--13",
journal = "European Journal of Control",
issn = "0947-3580",
publisher = "Lavoisier",
}