渐近稳定性蕴含局部多项式 Lyapunov 函数的存在性
最优化与控制
2012-01-23 v3
摘要
我们证明，任何具有二次连续可微向量场的全局渐近稳定系统，在原点的任意有界邻域内都存在一个局部多项式 Lyapunov 函数。
引用
@article{arxiv.1201.3311,
title = {Asymptotic stability implies the existence of a local polynomial Lyapunov function},
author = {M. Rungger and J. Kloos and R. Majumdar},
journal= {arXiv preprint arXiv:1201.3311},
year = {2012}
}
备注
There is a known counter-example. See "A Globally Asymptotically Stable Polynomial Vector Field with no Polynomial Lyapunov Function", by Amir Ali Ahmadi, Miroslav Krstic, and Pablo A. Parrilo, 50th IEEE Conference on Decision and Control. Our proof attempt will only work if there is a Lyapunov function such that the Hessian of its Lie derivative is negative definite in 0