# The geometry of Darlington synthesis (in memory of W. Cauer)

International Journal of Applied Mathematics and Computer Science (2001)

- Volume: 11, Issue: 6, page 1379-1386
- ISSN: 1641-876X

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topDewilde, Patrick. "The geometry of Darlington synthesis (in memory of W. Cauer)." International Journal of Applied Mathematics and Computer Science 11.6 (2001): 1379-1386. <http://eudml.org/doc/207560>.

@article{Dewilde2001,

abstract = {We revisit the classical problem of 'Darlington synthesis', or Darlington embedding. Although traditionally it is solved using analytic means, a more natural way to approach it is to use the geometric properties of a well-chosen Hankel map. The method yields surprising results. In the first place, it allows us to formulate necessary and sufficient conditions for the existence of the embedding in terms of systems properties of the transfer operation to be embedded. In addition, the approach allows us to extend the solution to situations where no analytical transform is available. The paper has a high review content, as all the results presented have been obtained during the last twenty years and have been published. However, we make a systematic attempt at formulating them in a geometric way, independent of an accidental parametrization. The benefit is clarity and generality.},

author = {Dewilde, Patrick},

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

keywords = {time-varying systems; coprime factorization; contractive operators; Darlington synthesis; Hankel operator; state space methods; time-varying case},

language = {eng},

number = {6},

pages = {1379-1386},

title = {The geometry of Darlington synthesis (in memory of W. Cauer)},

url = {http://eudml.org/doc/207560},

volume = {11},

year = {2001},

}

TY - JOUR

AU - Dewilde, Patrick

TI - The geometry of Darlington synthesis (in memory of W. Cauer)

JO - International Journal of Applied Mathematics and Computer Science

PY - 2001

VL - 11

IS - 6

SP - 1379

EP - 1386

AB - We revisit the classical problem of 'Darlington synthesis', or Darlington embedding. Although traditionally it is solved using analytic means, a more natural way to approach it is to use the geometric properties of a well-chosen Hankel map. The method yields surprising results. In the first place, it allows us to formulate necessary and sufficient conditions for the existence of the embedding in terms of systems properties of the transfer operation to be embedded. In addition, the approach allows us to extend the solution to situations where no analytical transform is available. The paper has a high review content, as all the results presented have been obtained during the last twenty years and have been published. However, we make a systematic attempt at formulating them in a geometric way, independent of an accidental parametrization. The benefit is clarity and generality.

LA - eng

KW - time-varying systems; coprime factorization; contractive operators; Darlington synthesis; Hankel operator; state space methods; time-varying case

UR - http://eudml.org/doc/207560

ER -

## References

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