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The stability of nonlinear systems in the region of linear dominance
Author(s) -
Gura I. A.,
Perlmutter D. D.
Publication year - 1965
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.690110321
Subject(s) - linearization , nonlinear system , stability (learning theory) , mathematics , computation , control theory (sociology) , class (philosophy) , computer science , physics , algorithm , control (management) , quantum mechanics , machine learning , artificial intelligence
A technique has been developed for finding quantitative regions of asymptotic stability for nonlinear systems by using a known proof of the theorem which substantiates the linearization. In a sense, the method defines a region in which the first‐order approximation is dominant from the point of view of stability. While the computations necessary can be somewhat involved, the procedure is essentially identical in all situations, and once established, can easily be used for a vast class of autonomous systems. The practical problems of both reversible and irreversible chemical reactions occuring in a continuous flow stirred vessel have been analyzed. Stability regions were obtained which are sufficiently extensive to be practical from the process viewpoint.