Stability robustness of linear output feedback systems with both time-varying structured and unstructured parameter uncertainties as well as delayed perturbations
type: Item
instance of: scholarly article
title: Stability robustness of linear output feedback systems with both time-varying structured and unstructured parameter uncertainties as well as delayed perturbations
zbMATH Open document ID: 1071.93043
author: Shinn-Horng Chen
author: Jyh-Horng Chou
author: Liang-An Zheng
published in: Journal of the Franklin Institute
publication date: 2005-02-22T00:00:00Z
review text: The authors consider the time delay control system with uncertainties \[ \dot{x}(t) = (A_0+\sum_{i=1}^mk_i(t)A_i+\widetilde{A}(t))x(t) + \sum_{\ell=1}^h\sum_{i=1}^m k_i(t)[A_{\ell i}x(t-\tau_\ell) +B_{\ell i}u(t-\tau_\ell)] + \] \[ + (B_0+\sum_{i=1}^mk_i(t)B_i+\widetilde{B}(t))u(t) \] \[ y = (C_0+\sum_{i=1}^mk_i(t)C_i+\widetilde{C}(t))x(t) \] with \(k_i(t)\) accounting for structured uncertainties and \(\widetilde{A}\), \(\widetilde{B}\), \(\widetilde{C}\) for bounded unstructured uncertainties. This system is subject to the static output controller \(u = Ky\). Some sufficient robust stability conditions are obtained using a standard quadratic Lyapunov functional of the form \[ V(\phi) = \phi^T(0)P\phi(0) + \sum_1^h\int_{-\tau_j}^0\phi^T(\theta)D_j\phi(\theta)d\theta. \] Some examples of academic type are discussed and a comparison to previous known results is given.
reviewed by: Vladimir Răsvan
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 93C23
zbMATH DE Number: 2136791
zbMATH Keywords: time delay systems
zbMATH Keywords: output feedback
zbMATH Keywords: Lyapunov functional
zbMATH Keywords: structured uncertainties
zbMATH Keywords: unstructured uncertainties
zbMATH Keywords: robust stability
MaRDI profile type: Publication
full work available at URL: j.jfranklin.2004.10.001
OpenAlex ID: W1986315463
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DOI: 10.1016/J.JFRANKLIN.2004.10.001
description: scientific article; zbMATH DE number 2136791