On the polystability of dynamical systems
type: Item
instance of: scholarly article
title: On the polystability of dynamical systems
zbMATH Open document ID: 0823.34055
author: Vladislav A. Martynyuk
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-11-06T00:00:00Z
review text: A partitioned system \(dx_ i/dt = f_ i(t,x_ 1, \dots, x_ s)\) with \(f_ i (t,x_ 1, \dots, x_ s) = 0\) for all \(t\) if and only if \(x_ 1 = \cdots = x_ n = 0\), \(x_ i \in \mathbb{R}^{n_ i}\), \(i = 1, \dots, s\), \(n_ 1 + \cdots + n_ s = n\), is said to be polystable if its zero solution \(x = 0 \in \mathbb{R}^ n\) is stable and attractive with respect to certain groups of variables \((x_ 1, \dots, x_ \ell)\), \(\ell \leq s\). The author gives sufficient conditions for polystability in terms of a Lyapunov function in the particular case \(s = 2\).
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 755524
zbMATH Keywords: polystability
zbMATH Keywords: Lyapunov function
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1142
OpenAlex ID: W2095029993
DOI: 10.1006/JMAA.1995.1142
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description: scientific article; zbMATH DE number 755524