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A non‐smooth lower bound on ν
Author(s) -
Lemos Rodrigo G.S.,
Simões Alberto M.,
Apkarian Pierre
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.2898
Subject(s) - upper and lower bounds , singular value , dimension (graph theory) , scalar (mathematics) , mathematics , skew , matrix (chemical analysis) , value (mathematics) , mathematical optimization , computer science , feature (linguistics) , algorithm , combinatorics , mathematical analysis , statistics , geometry , telecommunications , linguistics , eigenvalues and eigenvectors , physics , materials science , philosophy , quantum mechanics , composite material
SUMMARY A non‐smooth optimization technique to directly compute a lower bound on the skew structured singular value ν is developed. As corroborated by several real‐world challenging applications, the proposed technique can provide tighter lower bounds when compared with currently available techniques. Moreover, in many cases, the determined lower bound equals the true value of ν . Thanks to the efficiency of the non‐smooth technique, the algorithm can be applied to problems involving even a significant number of uncertain parameters. Another appealing feature of the proposed non‐smooth approach is that the dimension of repeated scalar uncertainties in the overall structured uncertainty matrix has little impact on the computational time. The technique can be used to compute a lower bound on the structured singular value μ as well. Copyright © 2012 John Wiley & Sons, Ltd.