Branch-point placement
type: Item
instance of: scholarly article
title: Branch-point placement
zbMATH Open document ID: 0712.93024
DOI: 10.1016/0024-3795(90)90231-Z
author: J. Rossiter
author: Basil Kouvaritakis
published in: Linear Algebra and its Applications
publication date: 1990-01-01T00:00:00Z
review text: One possible way of controller design for a multivariable linear system with a square transfer matrix G(z) - or G(s) for a continuous time system - is based upon the eigenfunctions \(n_ i(z)\) and eigenvectors \(w_ i(z)\). In practical circumstances it is not very convenient to use the functions \(n_ i(z)\) and \(w_ i(z)\) but rather approximations for the power series in \(z^{-1}\) of the functions \(n_ i(z)\) and \(w_ i(z)\) are used. Truncations of these power series exhibit an appropriate approximate description of the plant G(z) provided that the so called branch points \(\phi\) are outside the unit circle in the complex plane. Here the branch points are defined as those points in \({\mathbb{C}}\) where eigenfunctions \(n_ i(z)\) meet. The above observation makes it desirable to introduce a compensator K (with constant entries) such that the resulting transfer matrix G(s)K has all branch points outside the unit circle. The paper contains suitable algorithms for obtaining this property and two illustrative examples conclude the work.
reviewed by: H. Nijmeijer
Mathematics Subject Classification ID: 93B60
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93B55
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 93C35
zbMATH DE Number: 4172846
zbMATH Keywords: characteristic loci
zbMATH Keywords: eigenvalue and eigenvector approximation
zbMATH Keywords: transfer matrix
zbMATH Keywords: branch points
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4172846