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A hybrid approach to nonlinear system stability and performance
Author(s) -
Nikolaou M.,
Manousiouthakis V.
Publication year - 1989
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.690350406
Subject(s) - nonlinear system , control theory (sociology) , stability (learning theory) , computation , computer science , operator (biology) , state space , physical system , state (computer science) , mathematics , control (management) , mathematical optimization , algorithm , artificial intelligence , biochemistry , chemistry , physics , statistics , quantum mechanics , repressor , machine learning , transcription factor , gene
The problems of stability and performance for nonlinear feedback systems are examined. A hybrid approach that combines input‐output and state‐space theories is proposed. Within this framework the notions of dynamic gain and dynamic incremental gain of a nonlinear operator are reexamined and their inability to accurately reflect the dynamic behavior of a physical system is demonstrated. The concepts of dynamic gain and dynamic incremental gain over sets are introduced and their connection to a physical system's dynamic behavior is established. Theorems are developed that allow the systematic computation of these gains through nonsmooth optimal control theory. Illustrative examples are provided throughout the paper.