A new parameter estimate in singular perturbations
type: Item
instance of: scholarly article
title: A new parameter estimate in singular perturbations
zbMATH Open document ID: 0567.93058
DOI: 10.1016/0167-6911(85)90040-4
author: Eyad H. Abed
published in: Systems \& Control Letters
publication date: 1985-01-01T00:00:00Z
full work available at URL: http://hdl.handle.net/1903/4380
review text: A new upper bound is obtained for the singular perturbation parameter of an asymptotically stable singularly perturbed system. General time- invariant systems with a single small parameter are considered. The paper employs a Riccati equation whose solution is known to facilitate the exact decoupling of fast and slow dynamics. An application of the Brouwer fixed point theorem to the Riccati equation and of Ljapunov's direct method to the fast and slow subsystems results in the desired upper bound. Computation of the estimate requires only the solution of two Ljypunov matrix equations.
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 93C99
Mathematics Subject Classification ID: 34D15
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 3906360
zbMATH Keywords: singularly perturbed system
zbMATH Keywords: Riccati equation
zbMATH Keywords: decoupling of fast and slow dynamics
zbMATH Keywords: Ljypunov matrix equations
MaRDI profile type: Publication
OpenAlex ID: W2180472966
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description: scientific article; zbMATH DE number 3906360