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Peer-reviewedCC BY 4.0IEEE Transactions on Automatic Control

Linear Lyapunov Functions for Nonlinear Compartmental Systems

  • Sondre Wiersdalen
  • Mike Pereira
  • Annika Lang
  • Gabor Szederkényi
  • Jean Auriol
  • Balazs Kulcsar
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Abstract

This technical note examines exponential stability of the null solution to a large class of compartmental systems governed by ordinary differential equations. Sufficient conditions under which these systems admit a linear Lyapunov function are provided. The coefficients of the Lyapunov functions and the exponential decay rate they yield are obtained from an eigenvalue problem. For a special case of the system class considered, we derive an equivalence between attractivity of the null solution and the existence of a linear Lyapunov function.

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Cite

BibTeXRIS
BibTeX
@article{wiersdalen2026linear,
  title = {{Linear Lyapunov Functions for Nonlinear Compartmental Systems}},
  author = {Sondre Wiersdalen and Mike Pereira and Annika Lang and Gabor Szederkényi and Jean Auriol and Balazs Kulcsar},
  journal = {IEEE Transactions on Automatic Control},
  year = {2026},
  month = jun,
  doi = {10.1109/tac.2026.3708062},
  url = {https://hal.science/hal-05781977v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Linear Lyapunov Functions for Nonlinear Compartmental Systems
AU  - Sondre Wiersdalen
AU  - Mike Pereira
AU  - Annika Lang
AU  - Gabor Szederkényi
AU  - Jean Auriol
AU  - Balazs Kulcsar
PY  - 2026
DA  - 2026/06/26
JO  - IEEE Transactions on Automatic Control
DO  - 10.1109/tac.2026.3708062
UR  - https://hal.science/hal-05781977v1
AB  - This technical note examines exponential stability of the null solution to a large class of compartmental systems governed by ordinary differential equations. Sufficient conditions under which these systems admit a linear Lyapunov function are provided. The coefficients of the Lyapunov functions and the exponential decay rate they yield are obtained from an eigenvalue problem. For a special case of the system class considered, we derive an equivalence between attractivity of the null solution and the existence of a linear Lyapunov function.
SN  - 0018-9286
ER  -