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Stability of high dimensional nonlinear systems using Krasovskii's theorem
Author(s) -
Berger Albert J.,
Lapidus Leon
Publication year - 1969
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.690150209
Subject(s) - mathematics , nonlinear system , continuous stirred tank reactor , hypersurface , adiabatic process , stability (learning theory) , state variable , variable (mathematics) , liapunov function , derivative (finance) , mathematical analysis , control theory (sociology) , physics , thermodynamics , chemistry , computer science , control (management) , quantum mechanics , machine learning , artificial intelligence , financial economics , economics
Liapunov's direct method is used to establish a finite region of asymptotic stability for nonlinear systems with an arbitrary number of state variables. The procedure is a geometric one in multidimensional space which uses the Fletcher‐Powell minimization technique to find the maximum time derivative of the Liapunov function on the closed Liapunov hypersurface. Three detailed examples are presented, the first being the classical 2‐variable CSTR with heat transfer and the third being a 32‐variable 16‐stage model of an adiabatic tubular reactor with axial diffusion.