Technical Notes and Correspondence: Projection and Deflation Methods for Partial Pole Assignment in Linear State Feedback

Youcef Saad

doi:10.1109/9.406

Technical Notes and Correspondence: Projection and Deflation Methods for Partial Pole Assignment in Linear State Feedback

Youcef Saad

Research output: Contribution to journal › Article › peer-review

83 Scopus citations

Abstract

Two projection methods are proposed for partial pole placement in linear control systems. These methods are of interest in the common situation where the system is very large and only a few of its poles must be assigned. The first method is based on computing an orthonormal basis of the left invariant subspace associated with the eigenvalues to be assigned and then solving a small inverse eigenvalue problem resulting from projecting the initial problem into that subspace. The second method can be regarded as a variant of the Wielandt deflation technique used in eigenvalue methods.

Original language	English (US)
Pages (from-to)	290-297
Number of pages	8
Journal	IEEE Transactions on Automatic Control
Volume	33
Issue number	3
DOIs	https://doi.org/10.1109/9.406
State	Published - Mar 1988
Externally published	Yes

Bibliographical note

Funding Information:
Manuscript received January 23, 1986; revised April 20, 1987. Paper recommended by Past Associate Editor, J. B. Pearson. This work was supported in part by the Office of Naval Research under Contract N00014-82-K-0184, by the Department of Energy under Contract DEAC02-81ER0996, and by the Army Research Office under Contract DAAG-29-83-017 7. The author is with the University of Illinois, Urbana, IL 61801-2932. IEEE Log Number 8716991.

Publisher link

10.1109/9.406

Find It

Find It at U of M Libraries

Cite this

@article{9635c48a30cb47118f685a54d644e7c0,

title = "Technical Notes and Correspondence: Projection and Deflation Methods for Partial Pole Assignment in Linear State Feedback",

abstract = "Two projection methods are proposed for partial pole placement in linear control systems. These methods are of interest in the common situation where the system is very large and only a few of its poles must be assigned. The first method is based on computing an orthonormal basis of the left invariant subspace associated with the eigenvalues to be assigned and then solving a small inverse eigenvalue problem resulting from projecting the initial problem into that subspace. The second method can be regarded as a variant of the Wielandt deflation technique used in eigenvalue methods.",

author = "Youcef Saad",

note = "Funding Information: Manuscript received January 23, 1986; revised April 20, 1987. Paper recommended by Past Associate Editor, J. B. Pearson. This work was supported in part by the Office of Naval Research under Contract N00014-82-K-0184, by the Department of Energy under Contract DEAC02-81ER0996, and by the Army Research Office under Contract DAAG-29-83-017 7. The author is with the University of Illinois, Urbana, IL 61801-2932. IEEE Log Number 8716991.",

year = "1988",

month = mar,

doi = "10.1109/9.406",

language = "English (US)",

volume = "33",

pages = "290--297",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

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

number = "3",

}

TY - JOUR

T1 - Technical Notes and Correspondence

T2 - Projection and Deflation Methods for Partial Pole Assignment in Linear State Feedback

AU - Saad, Youcef

N1 - Funding Information: Manuscript received January 23, 1986; revised April 20, 1987. Paper recommended by Past Associate Editor, J. B. Pearson. This work was supported in part by the Office of Naval Research under Contract N00014-82-K-0184, by the Department of Energy under Contract DEAC02-81ER0996, and by the Army Research Office under Contract DAAG-29-83-017 7. The author is with the University of Illinois, Urbana, IL 61801-2932. IEEE Log Number 8716991.

PY - 1988/3

Y1 - 1988/3

N2 - Two projection methods are proposed for partial pole placement in linear control systems. These methods are of interest in the common situation where the system is very large and only a few of its poles must be assigned. The first method is based on computing an orthonormal basis of the left invariant subspace associated with the eigenvalues to be assigned and then solving a small inverse eigenvalue problem resulting from projecting the initial problem into that subspace. The second method can be regarded as a variant of the Wielandt deflation technique used in eigenvalue methods.

AB - Two projection methods are proposed for partial pole placement in linear control systems. These methods are of interest in the common situation where the system is very large and only a few of its poles must be assigned. The first method is based on computing an orthonormal basis of the left invariant subspace associated with the eigenvalues to be assigned and then solving a small inverse eigenvalue problem resulting from projecting the initial problem into that subspace. The second method can be regarded as a variant of the Wielandt deflation technique used in eigenvalue methods.

UR - http://www.scopus.com/inward/record.url?scp=0023979476&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023979476&partnerID=8YFLogxK

U2 - 10.1109/9.406

DO - 10.1109/9.406

M3 - Article

AN - SCOPUS:0023979476

SN - 0018-9286

VL - 33

SP - 290

EP - 297

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 3

ER -

Technical Notes and Correspondence: Projection and Deflation Methods for Partial Pole Assignment in Linear State Feedback

Abstract

Bibliographical note

Publisher link

Find It

Other files and links

Fingerprint

Cite this