A mixed performance control problem of discrete-time linear stochastic systems is discussed and investigated subject to H2 and passivity performances in this paper. Based on Itô modeling approach, stochastic systems can be represented as deterministic difference equation with multiplicative noise term. For the stochastic systems, H2 minimization problem and passivity constraint are simultaneously considered to achieve minimum output energy and attenuation performance. Applying Lyapunov theory, some sufficient conditions are derived into extended Linear Matrix Inequality (LMI) form to apply convex optimization algorithm. Moreover, a mixed H2/Passivity performance controller can be designed such that asymptotical stability and required performances of closed-loop system are guaranteed in the mean square. Finally, some simulations are proposed to demonstrate effectiveness and applicability of the proposed design method.

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