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Classical converse theorems in Lyapunov's second method

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  • 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.
    Mathematics Subject Classification: Primary: 93D05, 93D30, 93D20; Secondary: 93D10.

    Citation:

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