Explicit controller formulas for LMI-based \(H_ \infty\) synthesis
type: Item
instance of: scholarly article
title: Explicit controller formulas for LMI-based \(H_ \infty\) synthesis
zbMATH Open document ID: 0855.93025
DOI: 10.1016/0005-1098(96)00033-7
author: Pascal Gahinet
published in: Automatica
publication date: 1997-02-04T00:00:00Z
review text: For a given linear time-invariant plant \(P(s)\) with state-space realization, we have to find an \(H_\infty\)-suboptimal, internally stabilizing controller \(u = K(s)y\) that makes the closed-loop \(L_2\) gain from the disturbance to the error signal less than a prescribed value. The design is based on linear matrix inequalities (LMI). The synthesis is performed in two steps: First, solve a system of three LMIs, where the unknowns are two symmetric matrices \(R\), \(S\) of size equal to the plant order. Second, given \(R\), \(S\) and the plant, compute the controller by solving another LMI called the controller LMI. For the second part the paper finds explicit formulas. These were implemented in the LMI Control Toolbox for use with MATLAB.
reviewed by: A.Vaněček
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93B40
Mathematics Subject Classification ID: 15A39
zbMATH DE Number: 930680
zbMATH Keywords: \(H_ \infty\)
zbMATH Keywords: linear matrix inequalities
zbMATH Keywords: MATLAB
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: 0005-1098(96)00033-7
OpenAlex ID: W2109439079
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description: scientific article; zbMATH DE number 930680