On the zeros of blocked linear systems with single and mixed frequency data

Mohsen Zamani; Wetian Chen; Brian D.O. Anderson; Manfred Deistler; Alexander Filler

doi:10.1109/CDC.2011.6160434

On the zeros of blocked linear systems with single and mixed frequency data

Mohsen Zamani^*, Wetian Chen, Brian D.O. Anderson, Manfred Deistler, Alexander Filler

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

10 Citations (Scopus)

Abstract

This paper studies properties of blocked systems resulting from blocking discrete linear systems with mixed frequency data. The focus is on the zeros of the blocked systems. We first establish results on the simpler single frequency case, where the unblocked linear systems have all data at the same frequency. In particular, an explicit relation between the system matrix of the unblocked linear systems and that of their corresponding blocked systems is derived. Based on this relation, it is shown that the blocked systems are zero free if and only if the related unblocked systems are zero free. Furthermore, it is illustrated that square systems have zeros generically, i.e. for generic parameter matrices, and the corresponding kernel is of dimension one. With the help of the results obtained for the single frequency case, we then identify a situation in which the blocked systems can be zero free.

Original language	English
Title of host publication	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4312-4317
Number of pages	6
ISBN (Print)	9781612848006
DOIs	https://doi.org/10.1109/CDC.2011.6160434
Publication status	Published - 2011
Event	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States Duration: 12 Dec 2011 → 15 Dec 2011

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Country/Territory	United States
City	Orlando, FL
Period	12/12/11 → 15/12/11

Access to Document

10.1109/CDC.2011.6160434

Cite this

Zamani, M., Chen, W., Anderson, B. D. O., Deistler, M., & Filler, A. (2011). On the zeros of blocked linear systems with single and mixed frequency data. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 (pp. 4312-4317). Article 6160434 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2011.6160434

Zamani, Mohsen ; Chen, Wetian ; Anderson, Brian D.O. et al. / On the zeros of blocked linear systems with single and mixed frequency data. 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. Institute of Electrical and Electronics Engineers Inc., 2011. pp. 4312-4317 (Proceedings of the IEEE Conference on Decision and Control).

@inproceedings{95a7fdc4952e4fcfa2b7aecb3035451d,

title = "On the zeros of blocked linear systems with single and mixed frequency data",

abstract = "This paper studies properties of blocked systems resulting from blocking discrete linear systems with mixed frequency data. The focus is on the zeros of the blocked systems. We first establish results on the simpler single frequency case, where the unblocked linear systems have all data at the same frequency. In particular, an explicit relation between the system matrix of the unblocked linear systems and that of their corresponding blocked systems is derived. Based on this relation, it is shown that the blocked systems are zero free if and only if the related unblocked systems are zero free. Furthermore, it is illustrated that square systems have zeros generically, i.e. for generic parameter matrices, and the corresponding kernel is of dimension one. With the help of the results obtained for the single frequency case, we then identify a situation in which the blocked systems can be zero free.",

author = "Mohsen Zamani and Wetian Chen and Anderson, {Brian D.O.} and Manfred Deistler and Alexander Filler",

year = "2011",

doi = "10.1109/CDC.2011.6160434",

language = "English",

isbn = "9781612848006",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "4312--4317",

booktitle = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011",

address = "United States",

note = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 ; Conference date: 12-12-2011 Through 15-12-2011",

}

Zamani, M, Chen, W, Anderson, BDO, Deistler, M & Filler, A 2011, On the zeros of blocked linear systems with single and mixed frequency data. in 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011., 6160434, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 4312-4317, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6160434

On the zeros of blocked linear systems with single and mixed frequency data. / Zamani, Mohsen; Chen, Wetian; Anderson, Brian D.O. et al.
2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. Institute of Electrical and Electronics Engineers Inc., 2011. p. 4312-4317 6160434 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - On the zeros of blocked linear systems with single and mixed frequency data

AU - Zamani, Mohsen

AU - Chen, Wetian

AU - Anderson, Brian D.O.

AU - Deistler, Manfred

AU - Filler, Alexander

PY - 2011

Y1 - 2011

N2 - This paper studies properties of blocked systems resulting from blocking discrete linear systems with mixed frequency data. The focus is on the zeros of the blocked systems. We first establish results on the simpler single frequency case, where the unblocked linear systems have all data at the same frequency. In particular, an explicit relation between the system matrix of the unblocked linear systems and that of their corresponding blocked systems is derived. Based on this relation, it is shown that the blocked systems are zero free if and only if the related unblocked systems are zero free. Furthermore, it is illustrated that square systems have zeros generically, i.e. for generic parameter matrices, and the corresponding kernel is of dimension one. With the help of the results obtained for the single frequency case, we then identify a situation in which the blocked systems can be zero free.

AB - This paper studies properties of blocked systems resulting from blocking discrete linear systems with mixed frequency data. The focus is on the zeros of the blocked systems. We first establish results on the simpler single frequency case, where the unblocked linear systems have all data at the same frequency. In particular, an explicit relation between the system matrix of the unblocked linear systems and that of their corresponding blocked systems is derived. Based on this relation, it is shown that the blocked systems are zero free if and only if the related unblocked systems are zero free. Furthermore, it is illustrated that square systems have zeros generically, i.e. for generic parameter matrices, and the corresponding kernel is of dimension one. With the help of the results obtained for the single frequency case, we then identify a situation in which the blocked systems can be zero free.

UR - http://www.scopus.com/inward/record.url?scp=84860662416&partnerID=8YFLogxK

U2 - 10.1109/CDC.2011.6160434

DO - 10.1109/CDC.2011.6160434

M3 - Conference contribution

SN - 9781612848006

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 4312

EP - 4317

BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

Y2 - 12 December 2011 through 15 December 2011

ER -

Zamani M, Chen W, Anderson BDO, Deistler M, Filler A. On the zeros of blocked linear systems with single and mixed frequency data. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. Institute of Electrical and Electronics Engineers Inc. 2011. p. 4312-4317. 6160434. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2011.6160434

On the zeros of blocked linear systems with single and mixed frequency data

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this