Open Access
2015 On the Relation between Phase-Type Distributions and Positive Systems
Kyungsup Kim
Abstr. Appl. Anal. 2015: 1-7 (2015). DOI: 10.1155/2015/731261


The relation between phase-type representation and positive system realization in both the discrete and continuous time is discussed. Using the Perron-Frobenius theorem of nonnegative matrix theory, a transformation from positive realization to phase-type realization is derived under the excitability condition. In order to explain the connection, some useful properties and characteristics such as irreducibility, excitability, transparency, and order reduction for positive realization and phase-type representation are discussed. In addition, the connection between the phase-type renewal process and the feedback positive system is discussed in the stabilization concept.


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Kyungsup Kim. "On the Relation between Phase-Type Distributions and Positive Systems." Abstr. Appl. Anal. 2015 1 - 7, 2015.


Published: 2015
First available in Project Euclid: 15 June 2015

zbMATH: 1350.93030
MathSciNet: MR3339672
Digital Object Identifier: 10.1155/2015/731261

Rights: Copyright © 2015 Hindawi

Vol.2015 • 2015
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