Linear Lyapunov Functions for Nonlinear Compartmental Systems
Journal article, 2026
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.
Compartmental systems
Stability Analysis
traffic flow theory
Linear Lyapunov Functions
traffic reaction model
Author
Sondre Chanon Wiersdalen
Chalmers, Electrical Engineering, Systems and control
Mike Pereira
Université Paris PSL
Annika Lang
University of Gothenburg
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Jean Auriol
University Paris-Saclay
Gabor Szederkenyi
Pázmány Péter Catholic University
Balázs Adam Kulcsár
Chalmers, Electrical Engineering, Systems and control
IEEE Transactions on Automatic Control
0018-9286 (ISSN) 1558-2523 (eISSN)
Vol. In PressAreas of Advance
Transport
Subject Categories (SSIF 2025)
Computational Mathematics
Mathematical Analysis
Control Engineering
DOI
10.1109/TAC.2026.3708062