On the second method of liapunov

Persidskii, S. K.

doi:10.1016/0021-8928(61)90095-8

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A Design Based On Supremum Of Trajectories1

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Cited by 4 publications

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“…First, the converse Lyapunov function method initiated in the works of [26], [32] is used, which is developed below for the needs of homogeneous systems. Lemma 1.…”

Section: A Design Based On Supremum Of Trajectoriesmentioning

confidence: 99%

Homogeneous Lyapunov Functions: From Converse Design to Numerical Implementation

Efimov¹,

Ushirobira²,

Moreno³

et al. 2018

SIAM J. Control Optim.

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“…First, the converse Lyapunov function method initiated in the works of [26], [32] is used, which is developed below for the needs of homogeneous systems. Lemma 1.…”

Section: A Design Based On Supremum Of Trajectoriesmentioning

confidence: 99%

Homogeneous Lyapunov Functions: From Converse Design to Numerical Implementation

Efimov¹,

Ushirobira²,

Moreno³

et al. 2018

SIAM J. Control Optim.

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“…Early results -pre-1950. Persidskii [84] provided the first general converse theorem when he demonstrated that, under the assumption that the origin is a stable equilibrium point, the function…”

Section: 1mentioning

confidence: 99%

Classical converse theorems in Lyapunov's second method

Kellett¹

2015

DCDS-B

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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.2010 Mathematics Subject Classification. Primary: 93D05, 93D30, 93D20; Secondary: 93D10.

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Théorie de la stabilité dans les équations difféerentielles ordinaires

Rouche

2010

Stability Problems

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On the second method of liapunov

Cited by 4 publications

References 0 publications

Homogeneous Lyapunov Functions: From Converse Design to Numerical Implementation

Homogeneous Lyapunov Functions: From Converse Design to Numerical Implementation

Classical converse theorems in Lyapunov's second method

Théorie de la stabilité dans les équations difféerentielles ordinaires

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