1. Structure at infinity and defect of transfer matrices with time-varying coefficients, with application to exact model-matching.
- Author
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Bourlès, Henri
- Subjects
- *
DIVISION rings , *DISCRETE-time systems , *TRANSFER matrix , *POLYNOMIALS - Abstract
We study the structure at infinity of transfer matrices with time-varying coefficients. Such transfer matrices have their entries in a skew field F of rational fractions, i.e. of quotients of skew polynomials. Any skew rational fraction is the quotient of two proper ones, the latter forming a ring F p r (a subring of F) on which a "valuation at infinity" is defined. A transfer matrix G has both a "generalized degree" and a valuation at infinity, the sum of which is the opposite of the "defect" of G. The latter was first defined by Forney in the time-invariant case to be the difference between the total number of poles and the total number of zeros of G (poles and zeros at infinity included and multiplicities accounted for). In our framework, which covers both continuous- and discrete-time systems, the classic relation between the defect and Forney's left- and right-minimal indices is extended to the time-varying case. The exact model-matching problem is also completely solved. These results are illustrated through an example belonging to the area of power systems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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