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On Positive Linear Volterra-Stieltjes Differential Systems

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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.

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Correspondence to P. H. Anh Ngoc.

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The first author is supported by the Alexander von Humboldt Foundation.

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Ngoc, P.H.A., Murakami, S., Naito, T. et al. On Positive Linear Volterra-Stieltjes Differential Systems. Integr. equ. oper. theory 64, 325–355 (2009). https://doi.org/10.1007/s00020-009-1692-z

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  • DOI: https://doi.org/10.1007/s00020-009-1692-z

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