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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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/731261 |
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| _version_ | 1850106809914753024 |
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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. |
| format | Article |
| id | doaj-art-4dd722fd59c946e4a9a7ee0e577c7b0e |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| 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 |