Classical Converse Theorems in Lyapunov's Second Method
Optimization and Control
2016-08-12 v2
Abstract
Lyapunov's second or direct method is one of the most widely used techniques for investigating stability properties of dynamical systems. This technique makes use of an auxiliary function, called a Lyapunov function, to ascertain stability properties for a specific system without the need to generate system solutions. An important question is the converse or reversability of Lyapunov's second method; i.e., given a specific stability property does there exist an appropriate Lyapunov function? We survey some of the available answers to this question.
Keywords
Cite
@article{arxiv.1502.04809,
title = {Classical Converse Theorems in Lyapunov's Second Method},
author = {Christopher M. Kellett},
journal= {arXiv preprint arXiv:1502.04809},
year = {2016}
}