# Time-variant Darlington synthesis and induced realizations

International Journal of Applied Mathematics and Computer Science (2001)

- Volume: 11, Issue: 6, page 1331-1360
- ISSN: 1641-876X

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topPik, Derk. "Time-variant Darlington synthesis and induced realizations." International Journal of Applied Mathematics and Computer Science 11.6 (2001): 1331-1360. <http://eudml.org/doc/207558>.

@article{Pik2001,

abstract = {For a block lower triangular contraction T, necessary and sufficient conditions are given in order that there exist block lower triangular contractions T\_\{1,1\}, T\_\{2,1\} and T\_\{2,2\} such that T\_\{1,1\} T U\_T = [ ] T\_\{2,1\} T\_\{2,2\} is unitary. For the case when T^*\_\{1,1\} and T\_\{2,2\} 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.},

author = {Pik, Derk},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {time-variant linear systems; contractive linear systems; Darlington synthesis; unitary contraction; nonstationary case; lower triangular contractions},

language = {eng},

number = {6},

pages = {1331-1360},

title = {Time-variant Darlington synthesis and induced realizations},

url = {http://eudml.org/doc/207558},

volume = {11},

year = {2001},

}

TY - JOUR

AU - Pik, Derk

TI - Time-variant Darlington synthesis and induced realizations

JO - International Journal of Applied Mathematics and Computer Science

PY - 2001

VL - 11

IS - 6

SP - 1331

EP - 1360

AB - For a block lower triangular contraction T, necessary and sufficient conditions are given in order that there exist block lower triangular contractions T_{1,1}, T_{2,1} and T_{2,2} such that T_{1,1} T U_T = [ ] T_{2,1} T_{2,2} is unitary. For the case when T^*_{1,1} and T_{2,2} 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.

LA - eng

KW - time-variant linear systems; contractive linear systems; Darlington synthesis; unitary contraction; nonstationary case; lower triangular contractions

UR - http://eudml.org/doc/207558

ER -

## References

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