Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Robust Control in Gap Metric

  • Li QiuEmail author
  • Di Zhao
Living reference work entry

Latest version View entry history

DOI: https://doi.org/10.1007/978-1-4471-5102-9_165-2


Robust control needs to start with a model of system uncertainty. What is a good uncertainty model? First it needs to capture the possible system perturbations and uncertainties. Second it needs to be mathematically tractable. The gap metric was introduced by Zames and El-Sakkary for this purpose. Its study climaxed in an award-winning paper by Georgiou and Smith. A modified gap, called the ν-gap, was later discovered by Vinnicombe and was shown to have advantages. When the plant and controller communicate through a non-ideal bidirectional channel, cascaded two-port networks can be utilized to model such a channel whose uncertainties are measured by the \(\mathcal {H}_\infty \) norm. With these descriptions of uncertainties in hand, robust stabilization issues can be nicely addressed.


Gap metric H-infinity control ν-gap metric Robust stabilization Uncertain system Networked control system Two-port network 
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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electronic and Computer EngineeringHong Kong University of Science and TechnologyHong Kong SARChina

Section editors and affiliations

  • Kemin Zhou
    • 1
  1. 1.Department of Electrical and Computer Engineering, Louisiana State UniversityBaton RougeUSA