Geodesic
Time-variant Darlington synthesis and induced realizations
International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) no. 6, pp. 1331-1360.

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For a block lower triangular contraction T, necessary and sufficient conditions are given in order that there exist block lower triangular contractions T1,1, T2,1 and T2,2 such that Ut= [ T1,1 T ] T2,1 T2,2 is unitary. For the case when T1,1* and T2,2 have dense ranges, all such embeddings are described. Each unitary embedding of UT induces a contractive realization of T, and various properties of this realization are characterized in terms of the unitary embedding.
Keywords: contractive linear systems, Darlington synthesis, time-variant linear systems
Mots-clés : system liniowy, synteza Darlingtona 
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     author = {Pik, D.},
     title = {Time-variant {Darlington} synthesis and induced realizations},
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Pik, D. Time-variant Darlington synthesis and induced realizations. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) no. 6, pp. 1331-1360. http://geodesic.mathdoc.fr/item/IJAMCS_2001_11_6_a6/