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Stability of the Convex Linear Combination of Positive Linear Systems
Author(s) -
Kaczorek Tadeusz
Publication year - 2013
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.549
Subject(s) - mathematics , convex combination , diagonal , linear system , exponential stability , diagonal matrix , stability (learning theory) , regular polygon , linear matrix inequality , stability theory , convex analysis , matrix (chemical analysis) , convex optimization , mathematical analysis , nonlinear system , mathematical optimization , computer science , geometry , physics , materials science , quantum mechanics , machine learning , composite material
The asymptotic stability of the convex linear combination of positive continuous‐time and discrete‐time linear systems is addressed. Necessary and sufficient conditions for the asymptotic stability of the convex linear combination are established. The notion of diagonal dominant matrices for M etzler matrices and nonnegative real matrices is introduced. It is shown that the convex linear combination is asymptotically stable if its matrices are diagonal dominant.