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arXiv · 1502.04809

Classical Converse Theorems in Lyapunov's Second Method

Christopher M. Kellett
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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.

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Christopher M. Kellett. 2015-02-17. Classical Converse Theorems in Lyapunov's Second Method. https://doi.org/10.3934/dcdsb.2015.20.2333

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