Efficient Verification of CPA Lyapunov Functions

Abstract

: Lyapunov functions can be used to characterize the stability and basins of attraction for dynamical systems, whose dynamics are defined by ordinary differential equations. Since the analytic generation of Lyapunov functions for nonlinear systems is a formidable task, one often resorts to numerical methods. In this paper we study the efficient verification of the conditions for a Lyapunov function using affine interpolation over a triangulation; the values of the Lyapunov function candidate at the vertices of the triangulation can be generated using various different formulas from converse theorems in the Lyapunov stability theory. Further, we give an implementation in C++ and demonstrate its efficiency and applicability.