Stability by linear approximation for time scale dynamical systems
type: Item
instance of: scholarly article
title: Stability by linear approximation for time scale dynamical systems
zbMATH Open document ID: 1366.34119
author: Sergey Kryzhevich
author: A. I. Nazarov
published in: Journal of Mathematical Analysis and Applications
publication date: 2017-02-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/1512.02272
review text: The paper focuses on the matter of stability for linear systems and small nonlinear perturbations of such systems on time scales. Firstly, the stability of a solution is obtained by applying a time scale version of the Gronwall-Bellman inequality, by first approximation. It is proved afterwards that a linear time scale system with bounded, uniformly regressive matrix of coefficients, can be embedded into a linear system of ODEs with a bounded matrix. Finally, an analog of Chetaev's theorem on instability by first approximation is provided for time scale systems. The authors have thus proven that when studying stability/instability, methods from the theory of non-autonomous linear ODEs can be used in the framework of time scale dynamical systems.
reviewed by: Bianca Satco
Mathematics Subject Classification ID: 34N05
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 6682129
zbMATH Keywords: time scale system
zbMATH Keywords: linearization
zbMATH Keywords: Lyapunov functions
zbMATH Keywords: Millionschikov rotations
zbMATH Keywords: stability
MaRDI profile type: Publication
OpenAlex ID: W2962822368
arXiv ID: 1512.02272
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DOI: 10.1016/J.JMAA.2017.01.012
description: scientific article