Classical Converse Theorems in Lyapunov's Second Method
By Christopher M. Kellett. 2015
91 citations recorded by the source corpus.
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.
Subfields: Aerospace Engineering, Control and Systems Engineering, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/04f2a52edaaa27afdb18ef7341a928370c7c93f5
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In Aerospace Engineering
In Control and Systems Engineering
In Statistical and Nonlinear Physics
Citations in the corpus
- Review on computational methods for Lyapunov functions (2015, methodology): “For converse theorems, establishing the existence of Lyapunov functions, see for example Krasovskĭi 1963 [139], Yoshizawa 1966 [228], Hahn 1967 [112], Lin, Sontag and Wang 1996 [152], Teel and Praly 2000 [220] as well as the review in this volume Kellett 2015 [132].”