Robust Stabilization in the Gap Metric

  • Tyrphon T. Georgiou
  • Malcolm C. Smith
Part of the Progress in Systems and Control Theory book series (PSCT, volume 6)


This paper presents a brief overview of certain recent results on the application of the gap metric to robust stabilization of feedback systems. A detailed exposition of this work is reported in [8] – [11]. Here we present an explicit formula for the radius of gap ball uncertainty that a feedback system can tolerate, and we give a solution to the problem of robustness optimization in the gap metric. We also address the problem of robust stabilization under simultaneous plant and controller uncertainty. Finally we discuss an example of an infinite dimensional (delay) system and we give an explicit closed form expression for the optimally robust controller with respect to gap ball uncertainty.


Feedback System Robust Stabilization Robust Controller Hankel Operator Infinite Dimensional System 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Tyrphon T. Georgiou
    • 1
  • Malcolm C. Smith
    • 2
  1. 1.Department of Electrical EngineeringUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of Electrical EngineeringThe Ohio State UniversityColumbusUSA

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