Linear Lyapunov Functions for Nonlinear Compartmental Systems
For researchers studying stability of compartmental systems (e.g., biological or chemical networks), this offers a practical tool to certify exponential stability using linear Lyapunov functions.
This paper provides sufficient conditions for a class of nonlinear compartmental systems to admit a linear Lyapunov function, with coefficients and decay rates derived from an eigenvalue problem, and establishes equivalence between attractivity and existence of such a function for a special case.
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.