On the Relation between Phase-Type Distributions and Positive Systems

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 excitabilit...

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Main Author: Kyungsup Kim
Format: Article
Language:English
Published: Wiley 2015-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2015/731261
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author Kyungsup Kim
author_facet Kyungsup Kim
author_sort Kyungsup Kim
collection DOAJ
description 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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spelling doaj-art-4dd722fd59c946e4a9a7ee0e577c7b0e2025-08-20T02:38:45ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/731261731261On the Relation between Phase-Type Distributions and Positive SystemsKyungsup Kim0Department of Computer Engineering, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon 305-764, Republic of KoreaThe 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.http://dx.doi.org/10.1155/2015/731261
spellingShingle Kyungsup Kim
On the Relation between Phase-Type Distributions and Positive Systems
Abstract and Applied Analysis
title On the Relation between Phase-Type Distributions and Positive Systems
title_full On the Relation between Phase-Type Distributions and Positive Systems
title_fullStr On the Relation between Phase-Type Distributions and Positive Systems
title_full_unstemmed On the Relation between Phase-Type Distributions and Positive Systems
title_short On the Relation between Phase-Type Distributions and Positive Systems
title_sort on the relation between phase type distributions and positive systems
url http://dx.doi.org/10.1155/2015/731261
work_keys_str_mv AT kyungsupkim ontherelationbetweenphasetypedistributionsandpositivesystems