ISSN:
1531-5878
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
Abstract The objective of this paper is to present an algebraic theory for analyzing the infinite structures of singular systems. The key concept used in the development is the so-called homogeneous form for polynomial and rational matrices, which can be seen as a generalization of the well-known notion of homogeneous form for matrix pencils. We show how familiar concepts such as matrix fraction description, infinite poles and zeros, irreducibility, and cancellation at infinity appear naturally in this framework. The characterizations for some of these concepts are derived in terms of homogeneous forms. Considering singular systems to be alternative representations for (possibly nonproper) rational matrices, we are able to relate the fundamental concepts of controllability and reconstructibility for singular systems to the concept of complete coprimeness for rational matrices, and to relate the concept of minimal order of singular systems to the concept of the McMillan degree of rational matrices. As an important result, the equivalence relations among the concepts of joint controllability and reconstructibility, minimal order, and complete irreducibility are established. Moreover, we show that for any rational matrix factorized in matrix fraction description, the determinantal degree of the denominator matrix is the McMillan degree of the rational matrix if and only if the matrix fraction description is completely irreducible.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01201216
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