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Linear Lyapunov Functions for Nonlinear Compartmental Systems

Year: 2026
Type: article
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.
DOI: 10.1109/tac.2026.3708062
Authors: Sondre Wiersdalen, Mike Pereira, Annika Lang, Gábor Szederkényi, Jean Auriol, Balázs Kulcsár
Institutions: Chalmers University of Technology, Université Paris Sciences et Lettres, École Nationale Supérieure des Mines de Paris, Pázmány Péter Catholic University, Centre National de la Recherche Scientifique, Université Paris-Saclay, Laboratoire des signaux et systèmes, CentraleSupélec
Language: English
Open Access status: hybrid
Estimated APC paid: $2,645
OpenAlex ID: W4389984231
FWCI:
Cites: 22
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Related to: 10