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

Tobias Leth, Christoffer Sloth, Rafał Wisniewski, Sriram Sankaranarayanan
2017 IFAC-PapersOnLine  
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. Abstract: In this paper we prove the convergence of an algorithm synthesising
more » ... 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. Abstract: 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. Abstract: 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.
doi:10.1016/j.ifacol.2017.08.339 fatcat:25l34y2zmnedzizy2x3yceioku