Robust Stability with Time-Varying Structured Uncertainty

Jeff S. Shamma

doi:10.1109/9.286248

Robust Stability with Time-Varying Structured Uncertainty

Jeff S. Shamma^*

^*Corresponding author for this work

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

143 Scopus citations

Abstract

We consider the problem of assessing robust stability in the presence of block-diagonally structured time-varying dynamic uncertainty. We show that robust stability holds only if there exist constant scalings which lead to a small gain condition. The notion of stability here is finite-gain stability over finite-energy signals. In sharp contrast to the case of time-invariant dynamic uncertainty, this result is not limited by the number uncertainty blocks. These results parallel previous results regarding finite-gain stability over persistent bounded signals.

Original language	English (US)
Pages (from-to)	714-724
Number of pages	11
Journal	IEEE Transactions on Automatic Control
Volume	39
Issue number	4
DOIs	https://doi.org/10.1109/9.286248
State	Published - Apr 1994
Externally published	Yes

Bibliographical note

Funding Information:
Manuscript received February 17, 1992; revised March 10, 1993. Recommended by Past Associate Editor D. S. Bemstein. This work was supported in part by AFOSR Research Initiation Grant 92-70 and NSF Grants ECS 9296074 and ECS-9258005. The author is with the Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, TX 78712. IEEE Log Number 9215719.

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

Access to Document

10.1109/9.286248

Cite this

@article{683e7c4f528940f28b3aa7a1b7c120c3,

title = "Robust Stability with Time-Varying Structured Uncertainty",

abstract = "We consider the problem of assessing robust stability in the presence of block-diagonally structured time-varying dynamic uncertainty. We show that robust stability holds only if there exist constant scalings which lead to a small gain condition. The notion of stability here is finite-gain stability over finite-energy signals. In sharp contrast to the case of time-invariant dynamic uncertainty, this result is not limited by the number uncertainty blocks. These results parallel previous results regarding finite-gain stability over persistent bounded signals.",

author = "Shamma, {Jeff S.}",

note = "Funding Information: Manuscript received February 17, 1992; revised March 10, 1993. Recommended by Past Associate Editor D. S. Bemstein. This work was supported in part by AFOSR Research Initiation Grant 92-70 and NSF Grants ECS 9296074 and ECS-9258005. The author is with the Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, TX 78712. IEEE Log Number 9215719.",

year = "1994",

month = apr,

doi = "10.1109/9.286248",

language = "English (US)",

volume = "39",

pages = "714--724",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

publisher = "Institute of Electrical and Electronics Engineers",

number = "4",

}

TY - JOUR

T1 - Robust Stability with Time-Varying Structured Uncertainty

AU - Shamma, Jeff S.

N1 - Funding Information: Manuscript received February 17, 1992; revised March 10, 1993. Recommended by Past Associate Editor D. S. Bemstein. This work was supported in part by AFOSR Research Initiation Grant 92-70 and NSF Grants ECS 9296074 and ECS-9258005. The author is with the Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, TX 78712. IEEE Log Number 9215719.

PY - 1994/4

Y1 - 1994/4

N2 - We consider the problem of assessing robust stability in the presence of block-diagonally structured time-varying dynamic uncertainty. We show that robust stability holds only if there exist constant scalings which lead to a small gain condition. The notion of stability here is finite-gain stability over finite-energy signals. In sharp contrast to the case of time-invariant dynamic uncertainty, this result is not limited by the number uncertainty blocks. These results parallel previous results regarding finite-gain stability over persistent bounded signals.

AB - We consider the problem of assessing robust stability in the presence of block-diagonally structured time-varying dynamic uncertainty. We show that robust stability holds only if there exist constant scalings which lead to a small gain condition. The notion of stability here is finite-gain stability over finite-energy signals. In sharp contrast to the case of time-invariant dynamic uncertainty, this result is not limited by the number uncertainty blocks. These results parallel previous results regarding finite-gain stability over persistent bounded signals.

UR - http://www.scopus.com/inward/record.url?scp=0028412889&partnerID=8YFLogxK

U2 - 10.1109/9.286248

DO - 10.1109/9.286248

M3 - Article

AN - SCOPUS:0028412889

SN - 0018-9286

VL - 39

SP - 714

EP - 724

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 4

ER -

Robust Stability with Time-Varying Structured Uncertainty

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this