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Asymptotic stability in the distribution of nonlinear stochastic systems with semi-Markovian switching

Hou, Zhenting and Hailing, Dong and Shi, Peng (2007) Asymptotic stability in the distribution of nonlinear stochastic systems with semi-Markovian switching. The Australia and New Zealand Industrial and Applied Mathematics Journal (ANZIAM), 49 (2). pp. 231-241. ISSN 1446-1811

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Abstract

In this paper, finite phase semi-Markov processes are introduced. By introducing variables and a simple transformation, every finite phase semi-Markov process can be transformed to a finite Markov chain which is called its associated Markov chain. A consequence of this is that every phase semi-Markovian switching system may be equivalently expressed as its associated Markovian switching system. Existing results for Markovian switching systems may then be applied to analyze phase semi-Markovian switching systems. In the following, we obtain asymptotic stability for the distribution of nonlinear stochastic systems with semi-Markovian switching. The results can also be extended to general semi-Markovian switching systems. Finally, an example is given to illustrate the feasibility and effectiveness of the theoretical results obtained.

Item Type: Article
Uncontrolled Keywords: ResPubID18772, phase distribution, semi-Markovian switching, associated Markov chain, asymptotic stability in distribution
Subjects: Faculty/School/Research Centre/Department > Institute for Logistics and Supply Chain Management (ILSCM)
FOR Classification > 0199 Other Mathematical Sciences Information Systems
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Depositing User: VUIR
Date Deposited: 26 Apr 2012 23:49
Last Modified: 26 Apr 2012 23:49
URI: http://vuir.vu.edu.au/id/eprint/3243
DOI: 10.1017/S1446181100012803
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Citations in Scopus: 0 - View on Scopus

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