Analytic system problems and \(J\)-lossless coprime factorization for infinite-dimensional linear systems
type: Item
instance of: scholarly article
title: Analytic system problems and \(J\)-lossless coprime factorization for infinite-dimensional linear systems
zbMATH Open document ID: 0876.93028
DOI: 10.1016/S0024-3795(96)00175-9
author: O. Diekmann
published in: Linear Algebra and its Applications
publication date: 1997-12-01T00:00:00Z
review text: Let \(G\in H_\infty\) be given; the following problem is considered: Find all \(Q_1,Q_2\in H_\infty\) such that \[ \left[\begin{matrix} R\\ I\end{matrix}\right]= \left[\begin{matrix} G_{11} &G_{12}\\ G_{21} & G_{12}\end{matrix}\right]\left[\begin{matrix} Q_1\\ Q_2\end{matrix}\right],\quad|R|_\infty<\gamma. \] The approach is the one in [\textit{M. Green}, SIAM J. Control Optimization 30, 522-547 (1992; Zbl 0756.93039)]; consisting in the equivalence to a \(J\)-spectral factorization problem. This approach gives at the matrix-transfer level a solution to both the discrete-time and the continuous-time case. The stable analytic problem is solved for transfer matrices with an impulse response \(h\) satisfying \[ \int^\infty_0 e^{\varepsilon t}|h(t)|dt<\infty. \] All the details of proofs are included in an internal report of the authors: Analytic system problems and \(J\)-lossless coprime factorization of infinite-dimensional systems, Rep. W-9218, Mathematics Inst., Univ. of Groningen, The Netherlands.
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 93C80
zbMATH DE Number: 1011321
zbMATH Keywords: \(H_ \infty\)-control
zbMATH Keywords: infinite-dimensional systems
zbMATH Keywords: \(J\)-spectral factorization
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1011321