Existence of minimal nonsquare J-symmetric factorizations for self-adjoint rational matrix functions
✍ Scribed by L Lerer; M.A Petersen; A.C.M Ran
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 244 KB
- Volume
- 379
- Category
- Article
- ISSN
- 0024-3795
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✦ Synopsis
In this paper we show that any rational matrix function having hermitian values on the imaginary axis, and with constant signature and constant pole signature admits a minimal symmetric factorization with possibly nonsquare factors. Our proof is based on a construction which shows that any such function can be extended (preserving its McMillan degree) to a function that admits J -symmetric factorization with square factors. Also, we consider other properties of the factors in J -symmetric factorizations. Particular attention is given to the study of the common invariant zero structure of these factors.