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The problem of constructing a lyapunov function

Journal of Applied Mathematics and Mechanics, 1985
An algorithm which, for a wide class of problems, enables a Lyapunov function with a negative-sign derivative to be reconstructed as a Lyapunov function with a negative-definite derivative, is proposed. This algorithm supplements the well-known method of reconstructing a Lyapunov function. Examples are considered.
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Stability analysis of sampled-data systems via novel Lyapunov functional method

Information Sciences, 2022
Zhaoliang Sheng, Bing Chen, Qg Wang
exaly  

Vector Lyapunov Functions

Journal of the Society for Industrial and Applied Mathematics Series A Control, 1962
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On the construction of Lyapunov functions. I

The author studies vector fields on finite-dimensional smooth manifolds. To construct a Lyapunov function related to an equilibrium of a vector field, he uses the concept of `pilot function' introduced by him in [Autom. Remote Control 61, No. 4, Part 1, 585--594 (2000); translation from Avtom. Telemekh. 2000, No. 4, 51--60 (2000; Zbl 1060.34505)].
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