Lyapunov Function Synthesis - Infeasibility and Farkas’ Lemma * * This work is supported by the Danish Council for Independent Research under grant number DFF - 4005-00452 in the project CodeMe.

摘要

In this paper we prove the convergence of an algorithm synthesising continuous piecewise-polynomial Lyapunov functions for polynomial vector fields defined on simplices. We subsequently modify the algorithm to sub-divide locally by utilizing information from infeasible linear problems. We prove that this modification does not destroy the convergence of the algorithm. Both methods are accompanied by examples.