In this chapter the problem of \(H_2\) optimal control of an impulsive controlled linear stochastic system subject to Markovian jumping and independent multiplicative and additive white noise perturbations is considered. In Sect. 7.1 we begin by defining a so-called \(H_2\) norm of jump linear stochastic systems. Such a norm serves as a measure of the effect of additive white noise perturbations over an output of the controlled system, and thus it will be used as a performance criterion for the considered optimal control problem in this chapter. Section 7.2 is devoted to the computation of the value of the proposed \(H_2\) norm. Such a value is characterized via solutions of some suitably defined non-homogeneous forward/backward generalized Lyapunov-type jump linear differential equations on the spaces of symmetric matrices (see Theorem 7.1). A second \(H_2\) norm definition is then introduced at the end of this section and also characterized via solutions of some suitably defined non-homogeneous forward/backward generalized Lyapunov-type jump linear differential equations (see Theorem 7.2). An interesting dwell-time relation between the two proposed \(H_2\) norms is then highlighted in Remark 7.6. By using the \(H_2\) norms’ characterization results, we then address the control synthesis part. Firstly (Sect. 7.3), the problem of optimization of \(H_2\) norms is solved under the assumption that full-state vector is available for measurements. One shows that among all stabilizing controllers of arbitrary dimension, the best performance is achieved by a zero-order controller. The corresponding feedback gain of the optimal controller is constructed based on the stabilizing solution of an adequately defined system of backward jump matrix linear differential equations with Riccati-type jumping operator (see Theorem 7.4). Secondly, the \(H_2\) optimization problem is solved under the assumption that only an output is available for measurements. The state-space realization of the \(H_2\) -optimal controller is then obtained in Theorem 7.6. The main tool used in the construction of the optimal controller is here also a Riccati-type equation. We finally apply the obtained results to the case of sampled-data linear stochastic systems (Sect. 7.5).