Stochastic stability of linear systems with semi-Markovian jump parameters

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Hou, Zhenting, 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


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.

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Item type Article
DOI 10.1017/S1446181100008294
Official URL
Subjects Historical > FOR Classification > 0102 Applied Mathematics
Historical > Faculty/School/Research Centre/Department > Institute for Logistics and Supply Chain Management (ILSCM)
Keywords ResPubID18845; stochastic stability, linear and nonlinear system control, Markovian jump parameters
Citations in Scopus 37 - View on Scopus
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