Journal ArticleDOI
An investigation of partial asymptotic stability
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TLDR
In this paper, the partial attraction of motion and the asymptotic stability of unperturbed motion were investigated on the assumption that there exists a Lyapunov function with a positive or negative definite derivative.About:
This article is published in Journal of Applied Mathematics and Mechanics.The article was published on 1991-01-01. It has received 10 citations till now. The article focuses on the topics: Asymptotic analysis & Asymptotic analysis.read more
Citations
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Journal ArticleDOI
On partial stability theory of nonlinear dynamic systems
TL;DR: In this article, conditions of stability and asymptotic stability of non-stationary systems with the continuous right-hand side of the system were obtained using the method of Lyapunov functions.
Partial stability, stabilization and control: a some recent results
TL;DR: In this paper, some recent results concerning partial stability, stabilization, and control for some mechanical systems (solid, gyrostat, point in gravitational field) are considered, and their applications to problems of partial stabilization, stabilization and control are given.
Journal ArticleDOI
The stability of the equilibrium position of a non-autonomous mechanical system
TL;DR: In this article, sufficient conditions for the asymptotic stability and instability of the equilibrium position of a holonomic mechanical system acted upon by the time-dependent forces are determined.
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Recursive partial stabilization: Backstepping and generalized strict feedback form
TL;DR: A generalized strict feedback form for partial stabilization is presented followed by stabilization process.
Journal ArticleDOI
Problems of the partial stability and detectability of dynamical systems
TL;DR: In this article, the conditions under which uniform stability (uniform asymptotic stability) with respect to a part of the variables of the zero equilibrium position of a non-linear non-stationary system of ordinary differential equations signifies uniform stability of this equilibrium position with respect the other, larger part of variables, which include an additional group of coordinates of the phase vector, are established.
References
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Book
Theory of Ordinary Differential Equations
TL;DR: The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable as discussed by the authors, which is a useful text in the application of differential equations as well as for the pure mathematician.
Book
Stability Theory by Liapunov’s Direct Method
TL;DR: Barachin and Krasovski as mentioned in this paper introduced the concept of Attractivity for non-autonomous equilibria and proposed an approach to construct Liapunov functions.
Journal ArticleDOI
Topological dynamics of an ordinary differential equation
TL;DR: By casing the conditions the author automatically improves many results, including the validity of the LaSalle invariance principle in stability for the nonautonomous system dx/dt = f(x,t).
Journal ArticleDOI
On the asymptotic stability by nondecrescent Ljapunov function
TL;DR: In this article, conditions suffisantes for stabilite asymptotique partielle de the solution nulle d'un systeme non autonome en utilisant une fonction auxiliaire additionnelle au lieu de la decrescence de la fonctions de Ljapunov.
Journal ArticleDOI
On partial asymptotic stability by the method of limiting equation
TL;DR: In this paper, the authors generalized the Barbashin-Krasovskij method to non-holonomic dissipative mechanical systems and extended it to nonautonomous differential equations.
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