This paper consider the inventory robust control problem with an uncertain demand and bounded control actions. The considered system deals with a nonlinear discrete-time stochastic model of a special structure. The robust control designing, consisting in the inventory product level minimization by the corresponding adjustment of the production rate, is shown to be converted into certain averaged attractive ellipsoid “minimization” problem under some specific constraints of BMI's (Bilinear Matrix Inequalities) type. The application of an adequate coordinate changing transforms these BMI's into a set of LMI's (Linear Matrix Inequalities) that permits to use directly the standard MATLAB - toolbox. The matrix generalization of the SLLN (Strong Law of Large Numbers) provides an instrument for the stochastic analyses of the considered process.