Error bound for non-zero initial condition using the singular perturbation approximation method
type: Item
instance of: scholarly article
title: Error bound for non-zero initial condition using the singular perturbation approximation method
zbMATH Open document ID: 1405.93158
author: Adnan Daraghmeh
author: Naji A. Qatanani
published in: Mathematics
publication date: 2018-12-18T00:00:00Z
review text: Summary: In this article, we present up to date results on the balanced model reduction techniques for linear control systems, in particular the singular perturbation approximation. One of the most important features of this method is it allows for an a-priori \(L^2\) and \(H^\infty\) bounds for the approximation error. This method has been successfully applied for systems with homogeneous initial conditions, however, the main focus in this work is to derive an \(L^2\) error bound for singular perturbation approximation for system with inhomogeneous initial conditions, extending the work by \textit{A. C. Antoulas} [Approximation of large-scale dynamical systems. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2005; Zbl 1112.93002)]. The theoretical results are validated numerically.
Mathematics Subject Classification ID: 93C70
Mathematics Subject Classification ID: 93B11
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93B36
zbMATH DE Number: 6994835
zbMATH Keywords: reciprocal system
zbMATH Keywords: singular perturbation approximation
zbMATH Keywords: error bound
zbMATH Keywords: nonhomogeneous system
MaRDI profile type: Publication
full work available at URL: math6110232
OpenAlex ID: W2898879928
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DOI: 10.3390/MATH6110232
description: scientific article; zbMATH DE number 6994835