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Chemical networks with inflows and outflows: A positive linear differential inclusions approach
Author(s) -
Angeli David,
De Leenheer Patrick,
Sontag Eduardo D.
Publication year - 2009
Publication title -
biotechnology progress
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.572
H-Index - 129
eISSN - 1520-6033
pISSN - 8756-7938
DOI - 10.1002/btpr.162
Subject(s) - exponential stability , differential inclusion , homogeneous , nonlinear system , exponential growth , mathematics , homogeneous differential equation , stability (learning theory) , linear differential equation , exponential function , differential equation , differential (mechanical device) , regular polygon , mathematical analysis , control theory (sociology) , physics , computer science , thermodynamics , combinatorics , ordinary differential equation , geometry , differential algebraic equation , control (management) , quantum mechanics , machine learning , artificial intelligence
Certain mass‐action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state‐dependent linear time‐varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009