Robust Stability with Time-Varying Structured Uncertainty

Jeff S. Shamma*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

142 Scopus citations


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 languageEnglish (US)
Pages (from-to)714-724
Number of pages11
JournalIEEE Transactions on Automatic Control
Issue number4
StatePublished - Apr 1994

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


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