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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Balanced realization of orthogonally symmetric transfer function matrices
TL;DR: Structural properties of minimal balanced realizations of orthogonally symmetric transfer function matrices are developed and these properties are used to formulate a computationally efficient algorithm for determining balancedrealizations of transfer function Matrices in this class.
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Generalized Bezoutian and matrix equations
Leonid Lerer,Miron Tismenetsky +1 more
TL;DR: In this paper, a generalized Bezoutian of two polynomials is introduced for a family of matrix polynomial equations, where each equation in one of these classes is coupled with a certain equation in the other class so that for each couple the generalized bezoutians corresponding to a solution (Y(λ), Z(λ)) of the equation in matrix poynomials are a solution of the matrix equation, and conversely, any solution X of the solution X is a generalized BEZoutian corresponding to the solution of a certain solution in matrix
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Minimal realizations of pseudo-positive and pseudo-bounded rational matrices
TL;DR: In this article, the congruence class of a Hermitian matrix is determined by the Oono-Imamura index of the pseudo-positive matrix function, and the connection with the matrix Cauchy index is established.
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Stable Invariant Lagrangian Subspaces: Factorization of Symmetric Rational Matrix Functions and Other Applications
André C. M. Ran,Leiba Rodman +1 more
TL;DR: In this paper, several applications of earlier results by the authors concerning various notions of stability of invariant lagrangian subspaces are studied, such as stability of symmetric minimal factorizations of real symmetric rational matrix functions, stability of factorization of matrix polynomials, and stably well-posed matricial boundary value problems with symmetries.
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Transfer functions and operator theory
TL;DR: In this paper, a variety of material taken from existing literature is used to show that transfer functions from systems theory serve as an important tool in dealing with certain problems in operator and matrix theory, and a striking feature of the results is their high degree of explicitness.
References
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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.