On symmetric rational transfer functions
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In this article, a detailed study of symmetric transfer functions is presented, and a detailed analysis of transfer functions can be found in Section 5.1.1]...About:
This article is published in Linear Algebra and its Applications.The article was published on 1983-04-01 and is currently open access. It has received 87 citations till now.read more
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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)
Book ChapterDOI
Principal component analysis of flexible systems--Open-loop case
TL;DR: In this paper, a generic class of flexible systems, characterized by finitely many lightly damped harmonic oscillators, is analyzed by means of the "open-loop principal component analysis", that is, singular value analysis and Gramian balancing.
Journal ArticleDOI
LQG balancing and reduced LQG compensation of symmetric passive systems
TL;DR: In this article, a technique for balancing a system in a closed-loop fashion is developed, which is referred to as "LQG balancing", for it assumes that the system to be balanced is closed up with a standard LQG feedback loop.
Journal ArticleDOI
Model reduction for state-space symmetric systems
TL;DR: In this paper, the model reduction problem for state-space symmetric systems is investigated, and it is shown that several model reduction methods, such as balanced truncations, balanced truncation which preserves the DC gain, optimal and sub-optimal Hankel norm approximations, inherit the state space symmetric property.
References
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Journal ArticleDOI
Spectral analysis of families of operator polynomials and a generalized Vandermonde matrix II: The infinite dimensional case
TL;DR: In this article, the existence of a common monic multiple for a given family of monic operator polynomials was studied and necessary and sufficient conditions for the existence were given in terms of the invertibility of a generalized Vandermonde operator matrix.
Journal ArticleDOI
Nonsingular factors of polynomial matrices and (A,B)-invariant subspaces
TL;DR: In this paper, it was shown that finding such factorizations is equivalent to finding $(A,B)$-invariant subspaces in the kernel of C where A, B, C are linear maps determined by a polynomial matrix.
Journal ArticleDOI
On a theorem of Hermite and Hurwitz
TL;DR: The Hermite-Hurwitz theorem as discussed by the authors computes the degree of a real rational function in terms of the signature of an associated quadratic form, known today as the Hankel matrix of ƒ.
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A Jordan factorization theorem for polynomial matrices
TL;DR: In this paper, it was shown that for a proper rational matrix W with factorizations W(O C(J)IB M72)-Pa) Q(X)N(X)-1, C consists of Jordan chains of M and B of J chains of N.