Qualitative analysis of nonlinear systems by the method of matrix Lyapunov functions
type: Item
instance of: scholarly article
title: Qualitative analysis of nonlinear systems by the method of matrix Lyapunov functions
zbMATH Open document ID: 0841.34057
published in: Rocky Mountain Journal of Mathematics
publication date: 1996-07-31T00:00:00Z
review text: The author studies the system (1) \(x'= f(t, x)\) on a domain in \(\mathbb{R}^n\). He develops the notion of a matrix Lyapunov function as a natural generalization of ordinary scalar and vector Lyapunov functions. The main application is to give sufficient conditions for the asymptotic stability of the origin for a large class of equations which are perturbations of (1), when (1) is a ``large scale'' system.
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 796929
zbMATH Keywords: matrix Lyapunov function
zbMATH Keywords: asymptotic stability
author: A. A. Martynyuk
reviewed by: Alan R. Hausrath
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072291
OpenAlex ID: W2095013285
cites work: Q3325585
cites work: Q4069088
cites work: The Lyapunov matrix-function
cites work: On application of the Lyapunov matrix-functions in the theory of stability
cites work: Q3913074
cites work: Q4276911
cites work: Qualitative analysis of large scale dynamical systems
cites work: Q4165204
DOI: 10.1216/RMJM/1181072291
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description: scientific article; zbMATH DE number 796929