On the asymptotic stability and instability of the zeroth solution of a non-autonomous system
type: Item
instance of: scholarly article
title: On the asymptotic stability and instability of the zeroth solution of a non-autonomous system
zbMATH Open document ID: 0584.70007
DOI: 10.1016/0021-8928(84)90082-0
author: A. S. Andreev
published in: Journal of Applied Mathematics and Mechanics
publication date: 1985-01-01T00:00:00Z
review text: The system \(x'=X(t,x)\) is considered in n-dimensional space where X is measurable in t for fixed x, continuous in x for fixed t and satisfies certain generalized boundedness and Lipschitz conditions such that the bound and the ''Lipschitz constant'' are functions of t satisfying some requirements. The existence of limiting equations is assumed and limiting functions of some Lyapunov functions are defined. Several stability theorems are proved under some conditions imposed upon the limiting equations and limiting Lyapunov functions. The results are applied to the motion of a solid of variable mass in a resistive medium, to the Lagrange equations of a mechanical system with time dependent constraints, and to the problem of synthetization of the control moment assuring the asymptotic stability of a given triaxial orientation of a solid with variable moments of inertia.
Mathematics Subject Classification ID: 70E15
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 3936565
zbMATH Keywords: generalized boundedness condition
zbMATH Keywords: Lipschitz conditions
zbMATH Keywords: limiting equations
zbMATH Keywords: limiting Lyapunov functions
zbMATH Keywords: motion of a solid of variable mass
zbMATH Keywords: time dependent constraints
zbMATH Keywords: asymptotic stability
zbMATH Keywords: triaxial orientation of a solid
zbMATH Keywords: variable moments of inertia
reviewed by: M. Farkas
MaRDI profile type: Publication
full work available at URL: 0021-8928(84)90082-0
OpenAlex ID: W1986960878
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description: scientific article; zbMATH DE number 3936565