A polynomial approach to Hankel norm and balanced approximations
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In this article, a unified approach to Hankel norm and balanced approximations is presented which is based on a combination of polynomial algebra and the geometry of invariant subspaces.About:
This article is published in Linear Algebra and its Applications.The article was published on 1991-02-15 and is currently open access. It has received 39 citations till now. The article focuses on the topics: Hankel matrix & Invariant polynomial.read more
Citations
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Journal ArticleDOI
The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)
Journal Article
Approximation of large-scale dynamical systems: an overview
Journal ArticleDOI
On the decay rate of Hankel singular values and related issues
TL;DR: This paper investigates the decay rate of the Hankel singular values of linear dynamical systems by relating the solution to a numerically low-rank Cauchy matrix determined by the poles of the system.
Journal ArticleDOI
Approximation of Large-Scale Dynamical Systems: An Overview
TL;DR: This talk will survey methods for the approximation of large-scale dynamical systems and conclude with a new result concerning model reduction with preservation of passivity which is appropriate for application to large- scale circuits arising in VLSI chip performance verification.
Journal ArticleDOI
The subspace Nevanlinna interpolation problem and the most powerful unfalsified model
Paolo Rapisarda,Jan C. Willems +1 more
TL;DR: In this article, a generalization of the tangential Nevanlinna interpolation problem is studied from a behavioral point of view, and necessary and sufficient conditions for its solvability and a characterization of all its solutions are derived.
References
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Book
The Theory of Matrices
TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
Journal ArticleDOI
Principal component analysis in linear systems: Controllability, observability, and model reduction
TL;DR: In this paper, it is shown that principal component analysis (PCA) is a powerful tool for coping with structural instability in dynamic systems, and it is proposed that the first step in model reduction is to apply the mechanics of minimal realization using these working subspaces.
Book
Bounded Analytic Functions
TL;DR: In this article, the Corona construction was used to construct Douglas algebra and interpolating sequences and Maximal Ideals were used to solve a set of problems in the Corona Construction.
Journal ArticleDOI
All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds†
TL;DR: In this paper, a complete characterization of all rational functions that minimize the Hankel-norm is derived, and the solution to the latter problem is via results on balanced realizations, all-pass functions and the inertia of matrices, all in terms of the solutions to Lyapunov equations.
Related Papers (5)
All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds†
Analytic properties of schmidt pairs for a hankel operator and the generalized schur-takagi problem
V M Adamjan,D. Z. Arov,M G Kreĭn +2 more