A necessary and sufficient condition in Lyapunov robust control
type: Item
instance of: scholarly article
title: A necessary and sufficient condition in Lyapunov robust control
zbMATH Open document ID: 0663.93025
DOI: 10.1007/BF00939573
author: S. H. Smith
published in: Journal of Optimization Theory and Applications
publication date: 1989-01-01T00:00:00Z
review text: We consider Lyapunov's equation \(PA+A^ TP+Q=0\), where Q is symmetric positive definite and A is in controllable companion form. We prove that a necessary and sufficient condition that A be stable is that the first row \(P_ 1\) of the P-matrix be a stable n-1 coefficient vector. This result is related to the minimum phase property of linear systems and is useful in designing robust controllers.
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 4085512
zbMATH Keywords: Lyapunov's equation
zbMATH Keywords: controllable companion form
zbMATH Keywords: necessary and sufficient condition
zbMATH Keywords: robust controllers
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00939573
OpenAlex ID: W2036340086
description: scientific article; zbMATH DE number 4085512