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Computation of the real structured singular value via pole migration
Author(s) -
Iordanov P.,
Halton M.
Publication year - 2014
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.3259
Subject(s) - solver , parametric statistics , computation , singular value , focus (optics) , mathematical optimization , computer science , upper and lower bounds , algorithm , value (mathematics) , feature (linguistics) , class (philosophy) , mathematics , artificial intelligence , mathematical analysis , linguistics , statistics , eigenvalues and eigenvectors , physics , philosophy , quantum mechanics , machine learning , optics
Summary The paper introduces a new computationally efficient algorithm to determine a lower bound on the real structured singular value μ . The algorithm is based on a pole migration approach where an optimization solver is used to compute a lower bound on real μ independent of a frequency sweep. A distinguishing feature of this algorithm from other frequency independent one‐shot tests is that multiple localized optima (if they exist) are identified and returned from the search. This is achieved by using a number of alternative methods to generate different initial conditions from which the optimization solver can initiate its search from. The pole migration algorithm presented has also been extended to determine lower bounds for complex parametric uncertainties as well as full complex blocks. However, the results presented are for strictly real and repeated parametric uncertainty problems as this class of problem is the focus of this paper and are in general the most difficult to solve. Copyright © 2014 John Wiley & Sons, Ltd.