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Computation of irreducible generalized state-space realizations
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An efficient, numerically stable procedure is presented for the computation of irreducible generalized state-space realizations from non-minimal ones using orthogonal similarity transformations.Abstract:
In this paper, an efficient, numerically stable procedure is presented for the computation of irreducible generalized state-space realizations from non-minimal ones. The order reduction is performed by removing successively the uncontrollable and the unobservable parts of the system. Each reduction is accomplished by the same basic algorithm which deflates the uncontrollable part of the system using orthogonal similarity transformations. Applications of the proposed procedure are also presented.read more
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References
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Book
Introduction to matrix computations
TL;DR: Rounding-Error Analysis of Solution of Triangular Systems and of Gaussian Elimination.
Journal ArticleDOI
An Algorithm for Generalized Matrix Eigenvalue Problems.
Cleve B. Moler,G. W. Stewart +1 more
TL;DR: A new method, called the QZ algorithm, is presented for the solution of the matrix eigenvalue problem $Ax = \lambda Bx$ with general square matrices A and B with particular attention to the degeneracies which result when B is singular.
Journal ArticleDOI
The generalized eigenstructure problem in linear system theory
TL;DR: The numerical aspects of a certain class of such algorithms-dealing with what the author calls generalized eigenstructure problems-are discussed and some new and/or modified algorithms are presented.