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Worst‐case stability and performance with mixed parametric and dynamic uncertainties
Author(s) -
Apkarian Pierre,
Noll Dominikus
Publication year - 2016
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/rnc.3628
Subject(s) - parametric statistics , mathematical optimization , upper and lower bounds , stability (learning theory) , convergence (economics) , computer science , set (abstract data type) , certificate , extension (predicate logic) , mathematics , algorithm , mathematical analysis , economics , programming language , economic growth , statistics , machine learning
Summary This work deals with computing the worst‐case stability and the worst‐case H ∞ performance of linear time‐invariant systems subject to mixed real‐parametric and complex‐dynamic uncertainties in a compact parameter set. Our novel algorithmic approach is tailored to the properties of the nonsmooth worst‐case functions associated with stability and performance, and this leads to a fast and reliable optimization method, which finds good lower bounds of μ . We justify our approach theoretically by proving a local convergence certificate. Because computing μ is known to be NP‐hard, our technique should be used in tandem with a classical μ upper bound to assess global optimality. Extensive testing indicates that the technique is practically attractive. Copyright © 2016 John Wiley & Sons, Ltd.