Robust control of linear systems subject to uncertain time-varying parameters.
type: Item
instance of: scholarly article
title: Robust control of linear systems subject to uncertain time-varying parameters.
zbMATH Open document ID: 1142.93001
author: F. Amato
published in: Lecture Notes in Control and Information Sciences
publication date: 2006-03-28T00:00:00Z
review text: This book provides a systematic treatment of the theory of robust control of dynamical systems. The robust stability problem for linear systems subject to time-varying memoryless uncertainties is thoroughly investigated, using an approach based on the Lyapunov state-space stability theory; the relations with input-output operator theory methods are also investigated. The author has chosen to consider only the problems for which a definitive solution has been found, having in mind researchers or engineers working in industries who want to apply these methodologies to practical control problems. The presentation is self contained, all proofs are given as well as real world examples. At the end of each chapter a short summary, a brief history of the development of the research concerning such topics and further references for alternative approaches other than the ones considered are given. The topic is so ``hot'' that new results have appeared after the book's publication, but up to that time the bibliography is quite complete. One could only suggest to add a few, classical results on slowly varying systems. The self contained presentation makes it suitable to be used for educational post-graduate purposes. The structure of the book is the following. Chapter 1 contains an introduction, in Chapter 2 the qualitative behaviour of solutions of an autonomous system of linear differential equations with time dependent coefficient matrix is discussed: necessary and sufficient conditions for existence and uniqueness of solutions, conditions guaranteeing the stability of the equilibrium, the role of the state transition matrix. Several notions of stability are stated, in particular uniform asymptotic stability and exponential stability. Chapter 3 is devoted to the Lyapunov stability analysis of an autonomous linear system whose coefficient matrix depends on a vector \(p\) of uncertain parameters whose time behaviour is unknown in a given hyper-box. The problem of quadratic \(D\…
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C41
Mathematics Subject Classification ID: 34H05
zbMATH DE Number: 5015855
zbMATH Keywords: robust control
zbMATH Keywords: linear systems
zbMATH Keywords: time varying uncertainties
reviewed by: A. M. Perdon
describes a project that uses: LMI toolbox
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5015855