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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Minimal Realizations and Pole-Zero Structure
Erschienen in: Factorization of Matrix and Operator Functions: The State Space Method
Verlag: Birkhäuser Basel
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In this chapter finite-dimensional systems are studied in terms of the zero or pole data of their transfer functions. In the first two sections we describe the local zero and pole data, and related Jordan chains, of a meromorphic
m×m
matrix function of which the determinant does not vanish identically. In the third section these results are used to construct minimal realizations of rational matrix functions in terms of the zero or pole data of the function. The fourth section deals with the notions of local degree of a transfer function and local minimality of a finite-dimensional system. The global versions of these notions are studied in the final section.