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This paper discusses the stochastic H2/H∞ control problem with state-dependent noise. By means of the stabilization, exact observability and stochastic detectability of stochastic systems, the infinite horizon stochastic H2/H∞ control design is developed. For the finite horizon H2/H∞ control problem, our results generalize the corresponding deterministic ones to the stochastic models. Finally, the observer-based suboptimal stochastic H2/H∞ control is discussed in which the state variables cannot be measured directly, and a feasible design algorithm is proposed.