Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems

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Karan, Mehmet, Shi, Peng and Kaya, Yalcin (2006) Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems. Automatica, 42 (12). pp. 2159-2168. ISSN 0005-1098

Abstract

This paper considers the robustness of stochastic stability of Markovian jump linear systems in continuous- and discrete-time with respect to their transition rates and probabilities, respectively. The continuous-time (discrete-time) system is described via a continuous-valued state vector and a discrete-valued mode which varies according to a Markov process (chain). By using stochastic Lyapunov function approach and Kronecker product transformation techniques, sufficient conditions are obtained for the robust stochastic stability of the underlying systems, which are in terms of upper bounds on the perturbed transition rates and probabilities. Analytical expressions are derived for scalar systems, which are straightforward to use. Numerical examples are presented to show the potential of the proposed techniques.

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Item type Article
URI https://vuir.vu.edu.au/id/eprint/3020
DOI https://doi.org/10.1016/j.automatica.2006.07.002
Official URL http://www.sciencedirect.com/science?_ob=MImg&_ima...
Subjects Historical > FOR Classification > 0906 Electrical and Electronic Engineering
Historical > FOR Classification > 0103 Numerical and Computational Mathematics
Historical > Faculty/School/Research Centre/Department > Institute for Logistics and Supply Chain Management (ILSCM)
Keywords ResPubID18815, Markovian jump systems, parameter uncertainty, robustness, stochastic stability
Citations in Scopus 189 - View on Scopus
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