Automatically Discovering Relaxed Lyapunov Functions for Polynomial Dynamical Systems

摘要

The notion of Lyapunov function plays a key role in design and verification of dynamical systems, as well as hybrid and cyber-physical systems. In this paper, to analyze the asymptotic stability of equilibrium of a dynamical system, we generalize standard Lyapunov functions to relaxed Lyapunov functions (RLFs), by considering higher order Lie derivatives. Furthermore, we present a relatively complete method for automatically discovering polynomial RLFs for polynomial dynamical systems (PDSs). Our method is relatively complete in the sense that it is able to discover all polynomial RLFs for any PDS by enumerating all polynomial templates.