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Stochastic stability of linear systems with semi-Markovian jump parameters

Hou, Zhenting and Luo, Jiaowan and Shi, Peng (2005) Stochastic stability of linear systems with semi-Markovian jump parameters. The ANZIAM Journal, 46 (3). pp. 331-340. ISSN 1446-1811

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Abstract

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.

Item Type: Article
Uncontrolled Keywords: ResPubID18845; stochastic stability, linear and nonlinear system control, Markovian jump parameters
Subjects: FOR Classification > 0102 Applied Mathematics
Faculty/School/Research Centre/Department > Institute for Logistics and Supply Chain Management (ILSCM)
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Depositing User: VUIR
Date Deposited: 30 May 2011 04:56
Last Modified: 01 Aug 2011 03:31
URI: http://vuir.vu.edu.au/id/eprint/2779
DOI: 10.1017/S1446181100008294
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Citations in Scopus: 5 - View on Scopus

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