A unified approach to fixed-order controller design via linear matrix inequalities
type: Item
instance of: scholarly article
title: A unified approach to fixed-order controller design via linear matrix inequalities
zbMATH Open document ID: 0918.93014
DOI: 10.1155/S1024123X9500007X
author: Tetsuya Iwasaki
author: Robert E. Skelton
published in: Mathematical Problems in Engineering
publication date: 1999-08-19T00:00:00Z
full work available at URL: https://eudml.org/doc/48198
review text: Summary: We consider the design of fixed-order (lor low-order) linear controllers which meet certain performance and/or robustness specifications. The following three problems are considered; covariance control as a nominal performance problem, \({\mathcal Q}\)-stabilization as a robust stabilization problem, and robust \(L_\infty\) control problem as a robust performance problem. All three control problems are converted to a single linear algebra problem of solving a linear matrix inequality (LMI) of the type \(BGC+ (BGC)^T+Q<0\) for the unknown matrix \(G\). Thus this paper addresses the fixed-order controller design problem in a unified way. Necessary and sufficient conditions for the existence of a fixed-order controller which satisfies the design specifications for each problem are derived, and an explicit controller formula is given. In any case, the resulting problem is shown to be a search for a (structured) positive definite matrix \(X\) such that \(X\in{\mathcal C}_1\) and \(X^{-1}\in{\mathcal C}_2\) where \({\mathcal C}_1\) and \({\mathcal C}_2\) are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.
Mathematics Subject Classification ID: 93B51
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 15A39
zbMATH DE Number: 1282735
zbMATH Keywords: performance
zbMATH Keywords: robustness
zbMATH Keywords: covariance control
zbMATH Keywords: robust stabilization
zbMATH Keywords: robust \(L_\infty\) control
zbMATH Keywords: linear matrix inequality
zbMATH Keywords: fixed-order controller design
zbMATH Keywords: nonconvex LMI problem
MaRDI profile type: Publication
OpenAlex ID: W2005035203
description: scientific article; zbMATH DE number 1282735