On Positive Linear Volterra-Stieltjes Differential Systems |
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Authors: | P H Anh Ngoc S Murakami T Naito J Son Shin Y Nagabuchi |
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Institution: | 1. Institute of Mathematics, Technical University Ilmenau, Weimarer Stra?e 25, 98693, Ilmenau, Germany 2. Department of Applied Mathematics, Okayama University of Science, Ridaicho, Okayama, 700-0005, Japan 3. Department of Mathematics, University of Electro-Communication, Chofu, Tokyo, 182-8585, Japan
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Abstract: | We first introduce the notion of positive linear Volterra-Stieltjes differential systems. Then, we give some characterizations
of positive systems. An explicit criterion and a Perron-Frobenius type theorem for positive linear Volterra-Stieltjes differential
systems are given. Next, we offer a new criterion for uniformly asymptotic stability of positive systems. Finally, we study
stability radii of positive linear Volterra-Stieltjes differential systems. It is proved that complex, real and positive stability
radius of positive linear Volterra-Stieltjes differential systems under structured perturbations coincide and can be computed
by an explicit formula. The obtained results in this paper include ones established recently for positive linear Volterra
integro-differential systems 36] and for positive linear functional differential systems 32]-35] as particular cases. Moreover,
to the best of our knowledge, most of them are new.
The first author is supported by the Alexander von Humboldt Foundation. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 45J05 Secondary 34K20 93D09 |
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