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

144 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

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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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.",

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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.

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ER -

Robust Stability with Time-Varying Structured Uncertainty

Abstract

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