w-Stability of feedback systems

Tryphon T. Georgiou, Malcolm C. Smith

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


This paper introduces the notion of w-stability of feedback systems. This is a generalization of a concept of well-posedness discussed by Willems. w-Stability requires that a feedback system should remain stable under a certain class of perturbations which may not be vanishingly small when measured by the gap metric. The paper derives necessary and sufficient conditions for a feedback system to be w-stable. Further, an investigation of well posedness is given for feedback systems where high frequency roll-off has been suppressed for modelling simplicity. This question is pertinent in standard PID control.

Original languageEnglish (US)
Pages (from-to)271-277
Number of pages7
JournalSystems and Control Letters
Issue number4
StatePublished - Nov 1989

Bibliographical note

Funding Information:
* This work was supported in part by the NSF under Grant Nos. ECS-8705291 and MIP-8708811.


  • PID control
  • Stability
  • modelling uncertainty
  • robustness
  • well-posedness


Dive into the research topics of 'w-Stability of feedback systems'. Together they form a unique fingerprint.

Cite this