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

Published online by Cambridge University Press:  17 February 2009

Zhenting Hou ,
Hailing Dong  and
Peng Shi
Zhenting Hou
Affiliation:
School of Mathematics Central South University, Changsha 410075 Hunan China; email: hailing_f1y@mail.csu.edu.cn.
Hailing Dong
Affiliation:
School of Mathematics Central South University, Changsha 410075 Hunan China; email: hailing_f1y@mail.csu.edu.cn.
Peng Shi
Affiliation:
Faculty of Advanced Technology University of Glamorgan, Pontypridd CF37 1DL UK
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Abstract

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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.

Keywords

phase distributionsemi-Markovian switchingassociated Markov chainasymptotic stability in distribution.
Type
Articles
Information
The ANZIAM Journal , Volume 49 , Issue 2 , October 2007 , pp. 231 - 241
Copyright
Copyright © Australian Mathematical Society 2007

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