On partial asymptotic stability by the method of limiting equation
type: Item
instance of: scholarly article
title: On partial asymptotic stability by the method of limiting equation
zbMATH Open document ID: 0571.34039
DOI: 10.1007/BF01766850
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1985-01-01T00:00:00Z
review text: The well-known Barbashin-Krasovskij theorem, which establishes asymptotic stability for the zero solution of a differential system by a Lyapunov function with a negative semi-definite derivative (with respect to the given system), is extended to the partial asymptotic stability in the sense of V. V. Rumyantsev. Contrary to the previous extensions by \textit{V. V. Rumyantsev} [Sympos. Math. 6, 243-265 (1971; Zbl 0226.34047)], \textit{A. S. Oziraner} [Prikl. Mat. Mekh. 37, 659-665 (1973; Zbl 0295.34046)] and \textit{C. Risito} [Ann. Mat. Pura Appl., IV. Ser. 84, 279-292 (1970; Zbl 0213.106)], the condition of the boundedness of the uncontrolled coordinates is replaced by that not requiring ''a priori'' knowledge of the solution. Moreover, some applications to the stability properties of the equilibrium of dissipative nonholonomic mechanical systems are given.
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 3910818
zbMATH Keywords: Barbashin-Krasovskij theorem
zbMATH Keywords: Lyapunov function
zbMATH Keywords: partial asymptotic stability
zbMATH Keywords: dissipative nonholonomic mechanical systems
author: László Hatvani
reviewed by: Milan Tvrdý
MaRDI profile type: Publication
cites work: Q5813400
cites work: Q4083358
cites work: Sull'estensione ai sistemi dissipativi del criterio di stabilita del Routh
cites work: Q5632961
cites work: On asymptotic stability and instability relative to a part of variables
cites work: Sulla stabilità asintotica parziale
cites work: On stability of motion of nonholonomic systems
cites work: The method of Ljapunov functions in the stability problem for motion with respect to a part of the variables
cites work: Stability theory by Liapunov's direct method
cites work: Topological dynamics of an ordinary differential equation
cites work: Topological dynamics of ordinary differential equations and Kurzweil equations
cites work: The limiting equations of nonautonomous ordinary differential equations
cites work: Q3704238
cites work: Q5558515
cites work: Q4179872
cites work: On asymptotic stability and instability of motion with respect to a part of the variables
full work available at URL: https://doi.org/10.1007/bf01766850
OpenAlex ID: W2053414040
Recommended article: Q3704238
Recommended article: Q3360532
Recommended article: Investigation of partial asymptotic stability and instability based on the limiting equations
Recommended article: An investigation of partial asymptotic stability
Recommended article: On the stability of the equation with a partial boundary value condition
Recommended article: Q4949253
Recommended article: Partial asymptotic stability of abstract differential equations
Recommended article: Q4008605
Recommended article: Q4869086
Recommended article: Q3781426
description: scientific article; zbMATH DE number 3910818