Analysis of \(H_ 2\) and \(H_ \infty\) performance of discrete periodically time-varying controllers
type: Item
instance of: scholarly article
title: Analysis of \(H_ 2\) and \(H_ \infty\) performance of discrete periodically time-varying controllers
zbMATH Open document ID: 0881.93023
DOI: 10.1016/S0005-1098(96)00224-5
author: Jingxin Zhang
author: Katsuhisa Furuta
author: Cichen Zhang
published in: Automatica
publication date: 1998-01-27T00:00:00Z
review text: The paper is concerned with \( H_2 \) and \( H_\infty \) performance for discrete linear periodically time-varying (LPTV) controllers for the control of linear time-invariant (LTI) plants. Under some assumptions which, in particular, guarantee that the closed-loop systems controlled by LPTV controllers do not include LTI systems as a subset, it is shown that for \(H_2\) control, an LTI controller can be found to provide strictly better control. A necessary and sufficient condition on the system time-varying response is given. In this case, LTI control can be strictly better than LPTV control. The results provide deeper insight into time-varying mechanism and clarify how the time-varying dynamics can act and degrade the system performance.
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93C99
Mathematics Subject Classification ID: 93C55
zbMATH DE Number: 1038726
zbMATH Keywords: frequency-response methods
zbMATH Keywords: \(H_ \infty\) control
zbMATH Keywords: \(H_ 2\) control
zbMATH Keywords: periodic controllers
zbMATH Keywords: lifting in frequency domain
zbMATH Keywords: system performance
zbMATH Keywords: transfer functions
reviewed by: O. I. Nikonov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1038726