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A class of extended continuoustime Markov jump linear systems is proposed in this study. The generality lies in that the discrete dynamics of the class of systems is described by a Markov stochastic process, but with only partially known transition probabilities, which relax the traditional assumption in Markov jump systems that all the transition probabilities must be known a priori. Moreover, in contrast with the uncertain transition probabilities studied recently, no structure (polytopic ones), bounds (normbounded ones) or ‘nominal’ terms (both) are required for the partially unknown elements in the transition rate matrix. The sufficient conditions for H_{∞} control are derived via the linear matrix inequality formulation such that the closedloop system is stochastically stable and has a guaranteed H_{∞} noiseattenuation performance. A tradeoff can be built using our approach between the difficulties to obtain all the transition probabilities and the systems performance benefits. A numerical example is provided to show the validity and potential of the developed theoretical results.
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http://iet.metastore.ingenta.com/content/journals/10.1049/ietcta.2008.0023
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