From polynomial matrices to markov parameters and back: Theory and numerical algorithms

We consider polynomial matrix representations of MIMO linear systems and their connection to Markov parameters. Specifically, we consider polynomial matrix models in an arbitrary operator ρ, and develop theory and numerical algorithms for transforming polynomial matrix models into Markov parameter m...

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Bibliographic Details
Published in:Linear algebra and its applications 2012-08, Vol.437 (3), p.783-808
Main Authors: Holzel, Matthew S., Bernstein, Dennis S.
Format: Article
Language:English
Subjects:
Algebra
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Linear systems
Markov parameters
Mathematics
Polynomial matrices
Probability and statistics
Probability theory and stochastic processes
Realization theory
Sciences and techniques of general use
Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications)
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Summary:We consider polynomial matrix representations of MIMO linear systems and their connection to Markov parameters. Specifically, we consider polynomial matrix models in an arbitrary operator ρ, and develop theory and numerical algorithms for transforming polynomial matrix models into Markov parameter models, and vice versa. We also provide numerical examples to illustrate the proposed algorithms.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2012.03.006