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This study investigates the finite horizon H 2/H ∞ control of time-varying stochastic Markov jump systems (SMJSs) with state, control and disturbance-dependent noise. Firstly, the stochastic bounded real lemma of SMJSs is established, which by itself has theoretical importance. Secondly, several necessary and sufficient conditions for H 2/H ∞ control of SMJSs are proposed by means of coupled generalised differential Riccati equations. Finally, two numerical examples are given to show the effectiveness of the obtained results.
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