Lyapunov functions of the mechanical energy type
type: Item
instance of: scholarly article
title: Lyapunov functions of the mechanical energy type
zbMATH Open document ID: 0619.70018
DOI: 10.1016/0021-8928(85)90002-4
author: I. Tereki
author: László Hatvani
published in: Journal of Applied Mathematics and Mechanics
publication date: 1985-01-01T00:00:00Z
review text: When examining the properties of the stability and asymptotic behaviour of a system a Lyapunov function is often used as the total mechanical energy of the system. By analogy with the division of the energy into kinetic and potential energy, it is proposed below to construct a Lyapunov function in the form of the sum of two subsidiary scalar functions, such that its derivative on account of the system is estimated using some kind of function of these subsidiary functions. We examine the case when the derivative of the Lyapunov function can also take positive values, and the equation of comparison the emerges from the estimate of the Lyapunov function does not permit a separation of variables. \textit{V. V. Rumjancev}'s theorem [ibid. 35, 105-110 (1971; Zbl 0265.34069).] on the asymptotic stability with respect to the velocities of the equilibrium position of a dissipative mechanical system is generalized on the basis of the results obtained.
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 70F25
zbMATH DE Number: 4005666
zbMATH Keywords: stability
zbMATH Keywords: Lyapunov function
zbMATH Keywords: total mechanical energy
zbMATH Keywords: subsidiary functions
zbMATH Keywords: separation of variables
zbMATH Keywords: asymptotic stability
zbMATH Keywords: equilibrium position
zbMATH Keywords: dissipative mechanical system
MaRDI profile type: Publication
full work available at URL: 0021-8928(85)90002-4
OpenAlex ID: W1983096443
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description: scientific article; zbMATH DE number 4005666