The Nyquist robust sensitivity margin for uncertain closed-loop systems

The Nyquist robust sensitivity margin is proposed as a new scalar indicator of robust stability that also provides a meaningful quantitative assessment of the worst sensitivity realized by the uncertain closed loop. After formulating and discussing in detail the underlying optimization problem requi...

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Bibliographic Details
Published in:International journal of robust and nonlinear control 2005-09, Vol.15 (14), p.619-634
Main Authors: A. Al-Shamali, Saleh, Ji, Baowei, D. Crisalle, Oscar, A. Latchman, Haniph
Format: Article
Language:English
Subjects:
real affine uncertainty structure
robust control
robust performance
robust sensitivity
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Summary:The Nyquist robust sensitivity margin is proposed as a new scalar indicator of robust stability that also provides a meaningful quantitative assessment of the worst sensitivity realized by the uncertain closed loop. After formulating and discussing in detail the underlying optimization problem required for the calculation of the margin, the approach is applied to the characterization of the robust stability of a closed‐loop featuring a linear system with an affine uncertainty structure and a parametric uncertainty set described by a real rectangular polytope. The capabilities of the methodology are illustrated through examples, which include an approach for quantifying alternative robustness margins, such as a parametric stability margin. The computational algorithm is systematic and can be carried out with high numerical precision. Copyright © 2005 John Wiley & Sons, Ltd.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.1013