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

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Hou, Zhenting, 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

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.

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Item type Article
URI https://vuir.vu.edu.au/id/eprint/3243
DOI https://doi.org/10.1017/S1446181100012803
Subjects Historical > Faculty/School/Research Centre/Department > Institute for Logistics and Supply Chain Management (ILSCM)
Historical > FOR Classification > 0199 Other Mathematical Sciences Information Systems
Keywords ResPubID18772, phase distribution, semi-Markovian switching, associated Markov chain, asymptotic stability in distribution
Citations in Scopus 10 - View on Scopus
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