Abstract Lyapunov functions are a fundamental tool to investigate the stability properties of equilibrium points in linear or nonlinear systems. Unfortunately, even if the existence of Lyapunov functions for asymptotically stable equilibrium points is guaranteed by converse Lyapunov theorems, the actual computation of the analytic expression of the function may be difficult or impossible. Herein we propose an approach to avoid the issue of finding an explicit solution of the Lyapunov partial differential inequality, providing a family of Lyapunov functions for linear and nonlinear systems.