Minimal Realizations of Linear Systems: The "Shortest Basis" Approach
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Forney-Minimal Realizations.pdf
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244.32 KB
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Author(s)
Forney, G. David, Jr.
Date Issued
January 2011
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Forney, G. David. “Minimal Realizations of Linear Systems: The "Shortest Basis" Approach.” IEEE Transactions on Information Theory 57.2 (2011): 726–737.
Version
Author's final manuscript
Abstract
Given a discrete-time linear system C, a shortest basis for C is a set of linearly independent generators for C with the least possible lengths. A basis B is a shortest basis if and only if it has the predictable span property (i.e., has the predictable delay and degree properties, and is non-catastrophic), or alternatively if and only if it has the subsystem basis property (for any interval J, the generators in B whose span is in J is a basis for the subsystem CJ). The dimensions of the minimal state spaces and minimal transition spaces of C are simply the numbers of generators in a shortest basis B that are active at any given state or symbol time, respectively. A minimal linear realization for C in controller canonical form follows directly from a shortest basis for C, and a minimal linear realization for C in observer canonical form follows directly from a shortest basis for the orthogonal system C[superscript ⊥]. This approach seems conceptually simpler than that of classical minimal realization theory.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1109/tit.2010.2094811
