The problem of mixed H_{2}/H_{∞} control is considered for a class of uncertain discretetime nonlinear stochastic systems. The nonlinearities are described by statistical means of the stochastic variables and the uncertainties are represented by deterministic normbounded parameter perturbations. The mixed H_{2}/H_{∞} control problem is formulated in terms of the notion of exponentially meansquare quadratic stability and the characterisations of both the H_{2} control performance and the H_{∞} robustness performance. A new technique is developed to deal with the matrix trace terms arising from the stochastic nonlinearities and the wellknown Sprocedure is adopted to handle the deterministic uncertainities. A unified framework is established to solve the addressed mixed H_{2}/H_{∞} control problem using a linear matrix inequality approach. Within such a framework, two additional optimisation problems are discussed, one is to optimise the H_{∞} robustness performance, and the other is to optimise the H_{2} control performance. An illustrative example is provided to demonstrate the effectiveness of the proposed method.
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