New dilated LMI characterizations for continuous-time multiobjective controller synthesis
type: Item
instance of: scholarly article
title: New dilated LMI characterizations for continuous-time multiobjective controller synthesis
zbMATH Open document ID: 1061.93040
author: Yoshio Ebihara
author: Tomomichi Hagiwara
published in: Automatica
publication date: 2005-02-23T00:00:00Z
review text: The authors' main objective is to extend to the continuous-time case a linear matrix inequality (LMI) stabilizability condition originally available in the discrete-time case only. The main feature of the LMI condition is a decoupling between Lyapunov variables (ensuring stability or performance) and controller variables. The extension proposed in this paper is only partial and incomplete, but covers a non-trivial multiobjective design problem mixing \(H_2\) performance and pole location in a given region. It is shown that this design problem can be formulated as a nonlinear matrix inequality. This matrix inequality is non-convex in general, but it becomes a convex LMI problem when fixing a scalar parameter. Interestingly, it is shown in Theorem 6 that this LMI is always less conservative than previously available LMI design conditions, irrespective of the choice of the scalar parameter. This is the main contribution of this technical communique.
reviewed by: Didier Henrion
Mathematics Subject Classification ID: 93B50
Mathematics Subject Classification ID: 93B40
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 15A39
Mathematics Subject Classification ID: 93B55
Mathematics Subject Classification ID: 93B36
zbMATH DE Number: 2137230
zbMATH Keywords: controller design
zbMATH Keywords: linear matrix inequalities
zbMATH Keywords: Lyapunov techniques
zbMATH Keywords: regional pole placement
zbMATH Keywords: stabilizability
zbMATH Keywords: multiobjective design
zbMATH Keywords: \(H_2\) performance
MaRDI profile type: Publication
full work available at URL: j.automatica.2004.06.009
OpenAlex ID: W2018594715
cites work: Continuous-time analysis, eigenstructure assignment, and H/sub 2/ synthesis with enhanced linear matrix inequalities (LMI) characterizations
cites work: Linear Matrix Inequalities in System and Control Theory
cites work: H/sub ∞/ design with pole placement constraints: an LMI approach
cites work: A linear matrix inequality approach to H∞ control
cites work: All controllers for the general \({\mathcal H}_ \infty\) control problem: LMI existence conditions and state space formulas
cites work: LMI-based controller synthesis: a unified formulation and solution
cites work: A new discrete-time robust stability condition
cites work: Extended H 2 and H norm characterizations and controller parametrizations for discrete-time systems
cites work: A new robust D-stability condition for real convex polytopic uncertainty
cites work: Multiobjective output-feedback control via LMI optimization
cites work: Improved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainty
DOI: 10.1016/J.AUTOMATICA.2004.06.009
description: scientific article; zbMATH DE number 2137230