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PreprintCC BY-NC-ND 4.0HAL

Strong Stability of Linear Functional Equations with Distributed Delays

  • Yacine Chitour
  • Felipe Gonçalves Netto
  • Guilherme Mazanti
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Abstract

This paper considers linear functional equations on ℝd with distributed delays defined by matrix-valued measures of bounded variation. More precisely, we are interested in providing conditions to ensure that the exponential stability of these systems is preserved under small changes of the parameters which define them. In the special case of difference equations, it is known that exponential stability is preserved under small perturbations of the matrices defining the system, but not of the delays, and an additional condition for preservation of exponential stability under perturbation of the delays is given by the Hale--Silkowski criterion (HSC). In this paper, we extend the treatment of these issues to more general systems. For that purpose, we first put forward an appropriate definition of perturbation on the delays and then propose a conjecture in the spirit of (HSC). We prove several partial results related to that conjecture.

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Cite

BibTeXRIS
BibTeX
@misc{chitour2026strong,
  title = {{Strong Stability of Linear Functional Equations with Distributed Delays}},
  author = {Yacine Chitour and Felipe Gonçalves Netto and Guilherme Mazanti},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  url = {https://hal.science/hal-05337430v2},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Strong Stability of Linear Functional Equations with Distributed Delays
AU  - Yacine Chitour
AU  - Felipe Gonçalves Netto
AU  - Guilherme Mazanti
PY  - 2026
DA  - 2026/10/02
PB  - HAL
UR  - https://hal.science/hal-05337430v2
AB  - This paper considers linear functional equations on ℝ^d with distributed delays defined by matrix-valued measures of bounded variation. More precisely, we are interested in providing conditions to ensure that the exponential stability of these systems is preserved under small changes of the parameters which define them. In the special case of difference equations, it is known that exponential stability is preserved under small perturbations of the matrices defining the system, but not of the delays, and an additional condition for preservation of exponential stability under perturbation of the delays is given by the Hale--Silkowski criterion (HSC). In this paper, we extend the treatment of these issues to more general systems. For that purpose, we first put forward an appropriate definition of perturbation on the delays and then propose a conjecture in the spirit of (HSC). We prove several partial results related to that conjecture.
ER  -