A New Proof to the Necessity of a Second Moment Stability Condition of Discrete-Time Markov Jump Linear Systems with Real States
This paper studies the second moment stability of a discrete-time jump linear system with real states and the system matrix switching in a Markovian fashion. A sufficient stability condition was proposed by Fang and Loparo (2002), which only needs to check the eigenvalues of a deterministic matrix a...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/642480 |
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| _version_ | 1832564774024511488 |
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| author | Qiang Ling Haojiang Deng |
| author_facet | Qiang Ling Haojiang Deng |
| author_sort | Qiang Ling |
| collection | DOAJ |
| description | This paper studies the second moment stability of a discrete-time jump linear system with real states and the system matrix switching in a Markovian fashion. A sufficient stability condition was proposed by Fang and Loparo (2002), which only needs to check the eigenvalues of a deterministic matrix and is much more computationally efficient than other equivalent conditions. The proof to the necessity of that condition, however, is a challenging problem. In the paper by Costa and Fragoso (2004), a proof was given by extending the state domain to the complex space. This paper proposes an alternative necessity proof, which does not need to extend the state domain. The proof in this paper demonstrates well the essential properties of the Markov jump systems and achieves the desired result in the real state space. |
| format | Article |
| id | doaj-art-adde4935d92c43e5a662a8f689b270c7 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-adde4935d92c43e5a662a8f689b270c72025-02-03T01:10:15ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/642480642480A New Proof to the Necessity of a Second Moment Stability Condition of Discrete-Time Markov Jump Linear Systems with Real StatesQiang Ling0Haojiang Deng1Department of Automation, University of Science and Technology of China, Anhui, Hefei 230027, ChinaNational Network New Media Engineering Research Center, Institute of Acoustics, Chinese Academy of Science, Beijing 100190, ChinaThis paper studies the second moment stability of a discrete-time jump linear system with real states and the system matrix switching in a Markovian fashion. A sufficient stability condition was proposed by Fang and Loparo (2002), which only needs to check the eigenvalues of a deterministic matrix and is much more computationally efficient than other equivalent conditions. The proof to the necessity of that condition, however, is a challenging problem. In the paper by Costa and Fragoso (2004), a proof was given by extending the state domain to the complex space. This paper proposes an alternative necessity proof, which does not need to extend the state domain. The proof in this paper demonstrates well the essential properties of the Markov jump systems and achieves the desired result in the real state space.http://dx.doi.org/10.1155/2012/642480 |
| spellingShingle | Qiang Ling Haojiang Deng A New Proof to the Necessity of a Second Moment Stability Condition of Discrete-Time Markov Jump Linear Systems with Real States Journal of Applied Mathematics |
| title | A New Proof to the Necessity of a Second Moment Stability Condition of Discrete-Time Markov Jump Linear Systems with Real States |
| title_full | A New Proof to the Necessity of a Second Moment Stability Condition of Discrete-Time Markov Jump Linear Systems with Real States |
| title_fullStr | A New Proof to the Necessity of a Second Moment Stability Condition of Discrete-Time Markov Jump Linear Systems with Real States |
| title_full_unstemmed | A New Proof to the Necessity of a Second Moment Stability Condition of Discrete-Time Markov Jump Linear Systems with Real States |
| title_short | A New Proof to the Necessity of a Second Moment Stability Condition of Discrete-Time Markov Jump Linear Systems with Real States |
| title_sort | new proof to the necessity of a second moment stability condition of discrete time markov jump linear systems with real states |
| url | http://dx.doi.org/10.1155/2012/642480 |
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