Abstract
Assume that G is a stable and invertible transfer function. If G -1 has a stabilizing J-lossless conjugator Θ, then
is stable. Due to Lemma 5.3, the zeros of H coincide with those of G-1 which are stable from the assumption that G is stable. Hence, H-1 is also stable. Writing the relation (6.1) as
we see that G is represented as the product of a J-lossless matrix Θ and a unimodular matrix H-1 . This is a factorization of G which is of fundamental importance in H∞ control theory.
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© 1997 Birkhäuser Boston
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Kimura, H. (1997). J-Lossless Factorizations. In: Chain-Scattering Approach to H∞ Control. Systems & Control: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4080-8_6
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DOI: https://doi.org/10.1007/978-1-4612-4080-8_6
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8642-4
Online ISBN: 978-1-4612-4080-8
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