Robust stability analysis of time-varying systems using time-varying quadratic forms

Jeff S. Shamma*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We consider the robust stability of time-varying linear systems subject to structured time-varying uncertainty. We provide an alternate proof of the result that robust stability holds if and only if a scaled small-gain condition holds asymptotically. The new proof employs an extension of the so-called S-procedure losslessness theorem to time-varying quadratic forms which is of independent interest.

Original languageEnglish (US)
Pages (from-to)13-17
Number of pages5
JournalSystems and Control Letters
Issue number1
StatePublished - Jan 9 1995
Externally publishedYes

Bibliographical note

Funding Information:
* Supported by grants from Eglin Air Force Base, NSF grants #ECS-9296074 and #ECS-9258005, and a University Research Institute Summer Research Award.


  • Quadratic forms
  • Robust stability
  • Structured uncertainty
  • Time-varying systems

ASJC Scopus subject areas

  • Mechanical Engineering
  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science(all)


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