ANZIAM J. 49 (2007), no. 2, pp. 231–241.

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

Zhenting Hou Hailing Dong Peng Shi
School of Mathematics
Central South University
Changsha
410075 Hunan
China
School of Mathematics
Central South University
Changsha
410075 Hunan
China
hailing_fly@mail.csu.edu.cn
Faculty of Advanced Technology
University of Glamorgan
Pontypridd CF37 1DL
UK
Received March 17, 2007; revised August 6, 2007

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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2000 Mathematics Subject Classification: primary 34A34; secondary 60K15
(Metadata: XML, RSS, BibTeX) MathSciNet: MR2376???
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