Implicit Lyapunov functions and isochrones of linear systems

Lyapunov's direct method is based on a Lyapunov function that explicitly depends on the system's state vector. This article describes implicit Lyapunov functions and corresponding stability theorems that are counterparts of the explicit case. We also define isochrones of linear systems and describe their relationship to implicit Lyapunov functions. Determining settling times is considered as an application.