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A condition number scaling policy for stability robustness analysis
Author(s) -
Chanh Nguyen T.,
Barton Geoffrey W.,
Perkins John D.,
Johnston Richard D.
Publication year - 1988
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690340716
Subject(s) - scaling , controllability , singular value , transfer function , norm (philosophy) , robustness (evolution) , mathematics , mathematical optimization , control theory (sociology) , computer science , control (management) , engineering , physics , biochemistry , eigenvalues and eigenvectors , geometry , chemistry , quantum mechanics , artificial intelligence , political science , law , electrical engineering , gene
The condition number of the process transfer function G ( s ) has been proposed and used as an indicator of the inherent controllability of a process even though it is a scale‐dependent quantity. A rapid suboptimal scaling policy known as G ‐balancing is developed for the case of the l 2 norm where the condition number is the ratio of the largest to the smallest singular value of G ( s ). For 2 × 2 systems, G ‐balancing gives the same optimal scaling as an available analytical solution. The higher order examples given compare the results of G ‐balancing with the known analytic results for l 2 norm optimal scaling.