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THE NYQUIST ROBUST STABILITY MARGIN—A NEW METRIC FOR THE STABILITY OF UNCERTAIN SYSTEMS
Author(s) -
Latchman Haniph A.,
Crisalle Oscar D.,
Basker V. R.
Publication year - 1997
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/(sici)1099-1239(199702)7:2<211::aid-rnc299>3.0.co;2-8
Subject(s) - nyquist stability criterion , nyquist–shannon sampling theorem , robustness (evolution) , eigenvalues and eigenvectors , nyquist plot , small gain theorem , perturbation (astronomy) , control theory (sociology) , mathematics , complex plane , singular value , stability (learning theory) , metric (unit) , computer science , mathematical analysis , physics , engineering , statistics , artificial intelligence , operations management , dielectric spectroscopy , chemistry , biochemistry , control (management) , quantum mechanics , machine learning , electrochemistry , parametric statistics , electrode , gene
The Nyquist robust stability margin k N is proposed as a new tool for analysing the robustness of uncertain systems. The analysis is done using Nyquist arguments involving eigenvalues instead of singular values, and yields exact necessary and sufficient conditions for robust stability. The concept of a critical line on the Nyquist plane is defined and used to calculate a critical perturbation radius which in turn is used to produce k N . The new approach gives alternatives to computing exact stability margins in some cases of highly directional uncertainty templates where other models are not applicable. © 1997 by John Wiley & Sons, Ltd.