Stochastic stability of semi-Markov jump linear systems: An LMI approach

The semi-Markov jump linear system is more general than the classic Markov jump linear system. In the semi-Markov jump linear systems, the governing stochastic process is not a Markov process, but a semi-Markov process. Instead of the exponential distribution for the sojourn-time in each mode in the...

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Bibliographic Details
Published in2011 50th IEEE Conference on Decision and Control and European Control Conference pp. 4668 - 4673
Main Authors Ji Huang, Yang Shi
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.2011
Subjects
Exponential distribution
Linear systems
Markov processes
Numerical stability
Stability analysis
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ISBN9781612848006
1612848001
ISSN0191-2216
DOI10.1109/CDC.2011.6161313

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Summary:The semi-Markov jump linear system is more general than the classic Markov jump linear system. In the semi-Markov jump linear systems, the governing stochastic process is not a Markov process, but a semi-Markov process. Instead of the exponential distribution for the sojourn-time in each mode in the jump linear system, the Weibull distribution is considered in this paper. By deriving the infinitesimal generator for the Lyapunov function of the semi-Markov jump linear system, the numerically testable sufficient conditions for stochastic stability of semi-Markov jump linear systems are obtained. Numerical examples are provided to validate the proposed sufficient stochastic stability conditions.
ISBN:9781612848006
1612848001
ISSN:0191-2216
DOI:10.1109/CDC.2011.6161313