Control of rational systems using linear-fractional representations and linear matrix inequalities
type: Item
instance of: scholarly article
title: Control of rational systems using linear-fractional representations and linear matrix inequalities
zbMATH Open document ID: 0857.93040
DOI: 10.1016/0005-1098(96)00071-4
author: Yanyan Li
published in: Automatica
publication date: 1996-12-09T00:00:00Z
review text: A nonlinear, time-invariant system \(\dot x=F(x)x+G(x)u\), \(y=H(x)+J(x)u\), where the matrices are rational functions, is transformed to a `linear-fractional representation' \[ \dot x=Ax+B_uu+B_pp, \qquad q=C_qx+D_{qu}u+D_{qp}p, \qquad y=C_yx+D_{yu}u+D_{yp}p, \] \(p=\text{diag} (x_1I_{r1},\dots,x_nI_{rn})\), i.e. as a linear time-invariant system with a feedback connection between some fictious vector input \(p\) and fictious vector output \(q\). The feedback matrix is linear in the state vector \(x\) and its integers \(r_1,\dots,r_n\) reflect the `degree of nonlinearity'. Both state-feedback and dynamic output-feedback controller synthesis are adressed. As an example a controlled Van der Pol system is stabilized.
reviewed by: A.Vaněček
Mathematics Subject Classification ID: 93B50
Mathematics Subject Classification ID: 15A39
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 946988
zbMATH Keywords: rational control systems
zbMATH Keywords: feedback controller synthesis
zbMATH Keywords: linear-fractional representation
zbMATH Keywords: nonlinear
MaRDI profile type: Publication
full work available at URL: 0005-1098(96)00071-4
OpenAlex ID: W1987011453
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description: scientific article; zbMATH DE number 946988