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Vol: 52(66) No: 1 / March 2007      

Stability Criteria for Positive Linear Systems
Mihaela-Hanako Matcovschi
Department of Automatic Control and Applied Informatics, Faculty of Automatic Control and Computer Science Technical University Gh. Asachi of Iasi, Bd. Mangeron 53A, 700050 Iasi, Romania, phone: +40-232-230751, e-mail: mhanako@delta.ac.tuiasi.ro
Octavian Pastravanu
Department of Automatic Control and Applied Informatics, Faculty of Automatic Control and Computer Science Technical University Gh. Asachi of Iasi, Bd. Mangeron 53A, 700050 Iasi, Romania, e-mail: opastrav@delta.ac.tuiasi.ro


Keywords: positive linear system, asymptotic stability, Stein inequality, Lyapunov inequality, Holder norm, matrix measure.

Abstract
The paper develops novel criteria for the stability analysis of positive linear systems. Unlike traditional approaches focusing on quadratic-type Lyapunov functions, we consider Lyapunov functions defined by arbitrary vector norms. We address the cases of both discrete-time and continuous-time dynamics. We derive necessary and sufficient conditions formulated as matrix norm or matrix measure inequalities. Our results generalize the classical Stein or Lyapunov matrix inequalities in the sense of association with non-quadratic Lyapunov functions.

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