| Issue |
ESAIM: M2AN
Volume 60, Number 1, January-February 2026
|
|
|---|---|---|
| Page(s) | 83 - 110 | |
| DOI | https://doi.org/10.1051/m2an/2025096 | |
| Published online | 30 January 2026 | |
Dynamic output-based feedback stabilizability for linear parabolic equations with memory
1
Department of Mathematics, Indian Institute of Technology Roorkee (IITR), Roorkee, Uttarakhand 247667, India
2
Univ. Lille, CNRS, Inria, UMR 8524 Laboratoire Paul Painlevé, F-59000 Lille, France
3
Johann Radon Institute for Computational and Applied Mathematics (RICAM), OeAW, Altenbergerstr. 69, 4040 Linz, Austria
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
3
April
2025
Accepted:
27
November
2025
The stabilizability of a general class of linear parabolic equations with a memory term, is achieve by explicit output feedback. The control input is given as a function of a state-estimate provided by an exponential dynamic Luenberger observer based on the output of sensor measurements. The numbers of actuators and sensors are finite. The feedback input and output injection operators are given explicitly involving appropriate orthogonal projections. For exponential kernels, exponential stabilizability can be achieved with the rate of the exponential kernel. The discretization and simulation of the controlled systems are addressed as well and results of simulations are reported showing the performance of the proposed dynamic output-based control feedback input. We include simulations for both exponential and weakly singular Riesz kernels, showing the success of the strategy in obtaining a stabilizing input.
Mathematics Subject Classification: 93D15 / 93B52 / 93-08 / 93-10 / 93C20
Key words: Parabolic equations with memory / dynamic output-feedback stabilization / continuous data assimilation / positive kernels / explicit feedback-input and output-injection operators
© The authors. Published by EDP Sciences, SMAI 2026
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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