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STABILITY IN DISTRIBUTION OF NONLINEAR SYSTEMS WITH TIME-VARYING DELAYS AND SEMI-MARKOVIAN SWITCHING

Part of: General theory in ordinary differential equations

Published online by Cambridge University Press:  01 July 2008

ZAIMING LIU  and
JUN PENG
ZAIMING LIU
Affiliation:
Department of Mathematical Sciences, Central South University, Changsha, Hunan 410075, China (email: pengjunlrx@yahoo.com.cn)
JUN PENG*
Affiliation:
Department of Mathematical Sciences, Central South University, Changsha, Hunan 410075, China (email: pengjunlrx@yahoo.com.cn)
*
✉For correspondence; e-mail: pengjunlrx@yahoo.com.cn
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Abstract

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There has recently been considerable interest in the stability of stochastic differential equations with Markovian switching, and a number of results have been achieved. However, due to the exponential sojourn time of Markovian chain at each state, there are many restrictions on existing results for practical application. In this paper, we explore the problem of stability in distribution of nonlinear systems with time-varying delays and semi-Markov switching. Unlike existing models, the new model takes into account noise, time-varying delays and semi-Markov switching. By means of stochastic analysis, functional analysis and inequality techniques, sufficient conditions are obtained to guarantee the stability of the systems concerned. The proposed results are new and extend existing ones.

Keywords

stochastic differential equationsstability in distributiondelayssemi-Markovian switching

MSC classification

Secondary: 34A45: Theoretical approximation of solutions
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 1 , July 2008 , pp. 31 - 44
Copyright
Copyright © Australian Mathematical Society 2009

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