The paper devises a H ∞ -norm theory for the CSVIU (control and state variations increase uncertainty) class of stochastic systems. This system model appeals to stochastic control problems to express the state evolution of a possibly nonlinear dynamic system restraint to poor modeling. Contrary to other H ∞ stochastic formulations that mimic deterministic models dealing with finite energy disturbances, the focus is on the H ∞ control with infinity energy disturbance signals. Thus, the approach portrays the persistent perturbations due to the environment more naturally. In this regard, it requires a refined connection between a suitable notion of stability and the systems’ energy or power finiteness. It delves into the control solution employing the relations between H ∞ optimization and differential games, connecting the worst-case stability analysis of CSVIU systems with a perturbed Lyapunov type of equation. The norm characterization relies on the optimal cost induced by the Min-Max control strategy. The rise of a pure saddle point is linked to the solvability of a modified Riccati-type equation in a form known as a generalized game-type Riccati equation, which yields the solution of the CSVIU dynamic game. The emerging optimal disturbance compensator produces inaction regions in the sense that, for sufficiently minor deviations from the model, the optimal action is constant or null in the face of the uncertainty involved. A numerical example illustrates the synthesis.