Abstract
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.
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Qiu, L., Zhao, D. (2019). Robust Control in Gap Metric. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_165-2
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DOI: https://doi.org/10.1007/978-1-4471-5102-9_165-2
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Latest
Robust Control in Gap Metric- Published:
- 26 September 2019
DOI: https://doi.org/10.1007/978-1-4471-5102-9_165-2
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Original
Robust Control in Gap Metric- Published:
- 06 March 2014
DOI: https://doi.org/10.1007/978-1-4471-5102-9_165-1