Control of uncertain sampled-data systems
type: Item
instance of: scholarly article
title: Control of uncertain sampled-data systems
zbMATH Open document ID: 0843.93006
author: Geir E. Dullerud
published in: Systems \& Control: Foundations \& Applications
publication date: 1996-01-14T00:00:00Z
review text: This research monograph provides a detailed treatment of uncertainty analysis for sampled-data systems in the context of systems control theory. Sampled-data systems refers to the hybrid system formed when continuous time and discrete time systems are interconnected. By uncertainty analysis the author means achievable performance in the presence of worst-case uncertainty and disturbances. The monograph evolved from the author's Ph.D. dissertation at Cambridge University. The theory is developed primarily in an operator-theoretic framework; the signal space of interest is \(L_2\). A significant portion of the monograph is devoted to analyzing robust stabilization with linear time-invariant (LTI) perturbations. The author develops a condition that characterizes robust stability to structured, and thus also unstructured, LTI perturbation. This robustness test is in terms of the structured singular values of an infinite-dimensional compact operator. The author also considers robust performance of sampled-data systems to structured perturbations. Solutions to these robust performance problems are pursued using the same operator-theoretic framework and machinery that is developed for the LTI robustness analysis. The main feature of each of these conditions is that they are finite-dimensional. The robust performance problem is also investigated with respect to three uncertainty classes: periodic, quasi-periodic, and arbitrary time-varying uncertainties.
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93C57
Mathematics Subject Classification ID: 93B35
zbMATH DE Number: 833373
zbMATH Keywords: sampled-data systems
zbMATH Keywords: performance
zbMATH Keywords: worst-case uncertainty
zbMATH Keywords: operator-theoretic framework
zbMATH Keywords: robust stabilization
zbMATH Keywords: structured singular values
reviewed by: M. Zuhair Nashed
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 833373