Numerical Properties of Trajectory Representations
of Polynomial Matrices
Keywords
- Canonical Forms
- Computer-Aided System Design
- Control System Design
- Data Structures
- Minimum-Data Representation
- Numerical Methods
- Polynomial Matrices
Abstract
In the early 1970s, several researchers reported results relating to the
design of multivariable linear systems represented by polynomial matrices. In
particular, the book by Wolovich (1974) found widespread resonance. In the
sequel, however, the success of these techniques was rather limited since a
manual application of the proposed algorithms is atrocious for all but the most
trivial systems, whereas appropriate CACSD tools that would make use of these
techniques were not available. The main reasons for this deficiency were
twofold: (i) polynomial matrix operations require symbolic processing, a
computational technique that was still in its infancy in the 1970s, and (ii)
the numerical properties of frequency domain operations were considered dubious.
In this paper, the numerical properties of frequency domain operations are
analyzed. The two classical data representations (coefficients and roots) are
reviewed, and two new data representations, trajectories and coefficient
spectra, are proposed.
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Last modified: December 15, 2005 -- © François Cellier