2015/02/17 by Christopher M. Kellett · 1 voice
Mathematics · #math.OC
paper · pdf · doi:10.3934/dcdsb.2015.20.2333
published as Discrete and Continuous Dynamical Systems Series B, v. 20, no. 8, October 2015
arxiv published 2015/02/17 · arxiv created 2016/08/11 · arxiv updated 2016/08/12
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.