This chapter is devoted to a the robust stability analysis, as well as to the problem of the robust stabilization of the class of impulsive Markovian jump linear systems subject to block-diagonal stochastic parameter perturbations. To the best of the authors knowledge, robust stabilization for linear impulsive stochastic systems has not been considered yet in the literature. In Sect. 9.1, a detailed description of the model of the system as well as the model of the considered class of structured stochastic uncertainties are given. The considered parametric uncertainties are of multiplicative white noise type with unknown intensity. In order to measure the level of the robustness of the stability of the considered class of impulsive systems with respect to the stochastic structured uncertainties we introduce in Sect. 9.2 the concept of stability radius. In order to effectively address the multiperturbations case, we use scaling techniques; hence in Sect. 9.3 we begin by a detailed description of such techniques when applied to our setting. By using these scaling techniques, we then succeed to obtain an estimation of the lower bound of the stability radius. A first characterization of a lower bound of the stability radius is obtained in terms of the unique bounded and positive semidefinite solutions of an adequately defined parameterized backward Lyapunov-type jump linear differential equations (Theorems 9.1 and 9.2). A second characterization is given in terms of the existence of positive definite solutions of adequately defined parameterized backward Lyapunov-type jump differential inequalities (Theorem 9.3). This second result is then exploited in order to solve a robust control synthesis problem in Sect. 9.4. A first answer to the robust control problem is obtained in Theorem 9.5 where the stabilizing feedback gains are characterized via the solution of an adequately defined nonlinear backward jumps matrix differential inequality. The nonlinear nature of the conditions obtained in Theorem 9.5 makes there numerical exploitation not tractable. Hence, a second answer (numerically tractable) to the robust control problem is proposed in Corollary 9.3 where the stabilizing feedback gains are characterized via the unique stabilizing solution of an adequately defined backward jumps matrix Lyapunov differential equation with Riccati-type jumping operator. We finally apply the obtained results to the case of sampled-data linear stochastic systems (Sect. 9.5).