Stability of the Convex Linear Combination of Positive Linear Systems

descriptionPublicationkeyboard_double_arrow_right Article 05 Jul 2012 English Publisher:WileyJournal:Asian Journal of Control, volume 15, pages 1,850-1,857 (issn: 1561-8625, eissn: 1934-6093,

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Authors: Kaczorek, Tadeusz;

doi: 10.1002/asjc.549

Stability of the Convex Linear Combination of Positive Linear Systems

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Abstract

AbstractThe 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 Metzler matrices and nonnegative real matrices is introduced. It is shown that the convex linear combination is asymptotically stable if its matrices are diagonal dominant.

Keywords

Asymptotic stability in control theory, asymptotic stability, positive systems, Discrete-time control/observation systems, Linear systems in control theory, Metzler matrix, convex linear combination, nonnegative matrix, Control/observation systems governed by ordinary differential equations

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