On parametric stabilization of uncertain singularly perturbed systems
type: Item
instance of: scholarly article
title: On parametric stabilization of uncertain singularly perturbed systems
zbMATH Open document ID: 1278.34069
author: A. S. Khoroshun
author: A. A. Martynyuk
published in: Journal of Mathematical Sciences (New York)
publication date: 2013-07-30T00:00:00Z
review text: A linear uncertain singularly perturbed system whose trivial solution is unstable for the values of a parameter from a certain domain, is considered. The problem is to parametrically stabilize the original system, i.e. to choose a control that guarantees the absolute stability of a moving equilibrium state of the obtained nonlinear uncertain singularly perturbed system for all values of the parameter from a certain domain and to determine this domain. The obtained nonlinear singularly perturbed system allows one to choose a degenerate subsystem and a boundary layer. However, they do not enable one to construct the components of a Lyapunov vector function and to verify the stability of the original system because of the absence of information on the stability of these subsystems. That is why, in this paper, a matrix-valued Lyapunov function is used for the investigation of the absolute parametric stability of uncertain singularly perturbed systems.
reviewed by: Vasile Dragan
Mathematics Subject Classification ID: 34H15
Mathematics Subject Classification ID: 34D15
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 93C70
Mathematics Subject Classification ID: 93C41
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 6192522
zbMATH Keywords: uncertain singularly perturbed systems
zbMATH Keywords: absolute parametric stability
zbMATH Keywords: matrix valued Lyapunov function
zbMATH Keywords: degenerate subsystem
zbMATH Keywords: boundary layer
MaRDI profile type: Publication
full work available at URL: s10958-013-1326-5
OpenAlex ID: W2035258529
cites work: Q3651921
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cites work: Q3826925
DOI: 10.1007/S10958-013-1326-5
description: scientific article; zbMATH DE number 6192522