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Stochastic stability of linear systems with semi-Markovian jump parameters

Published online by Cambridge University Press:  17 February 2009

Zhenting Hou ,
Jiaowan Luo  and
Peng Shi
Zhenting Hou
Affiliation:
School of Mathematics, Central South University, Changsha, Hunan 410075, China; e-mail: zthou@csu.edu.cn.
Jiaowan Luo
Affiliation:
School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario KIS 5B6, Canada; e-mail: jwluo@math.carleton.ca.
Peng Shi
Affiliation:
School of Technology, University of Glamorgan, Pontypridd, Wales, CF37 1DL, UK; e-mail: pshi@glam.ac.uk.
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Abstract

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Over the past two decades considerable effort has been devoted to problems of stochastic stability, stabilisation, filtering and control for linear and nonlinear systems with Markovian jump parameters, and a number of results have been achieved. However, due to the exponential distribution of the Markovian chain, there are many restrictions on existing results for practical applications. In the present paper, we study systems whose jump parameters are semi-Markovian rather than fully Markovian. We consider only linear systems with semi-Markovian jump parameters, and also study systems with phase-type semi-Markovian jump parameters, because the family of phase-type distributions is dense in the families of all probability distributions on [0, +∞). Some stochastic stability results are obtained. An example is given to show the potential of the proposed techniques.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 3 , January 2005 , pp. 331 - 340
Copyright
Copyright © Australian Mathematical Society 2005

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