Output dynamic controller analysis for stochastic systems of multiplicative type

The most important unsolved problem of control theory is the problem of optimizing a multiplicative stochastic system in the class of noisy output signal controllers. The controller in the feedback loop must be feasible; i.e., it must ensure the stability of the closed-loop system and guarantee the required level of suppression of exogenous disturbances acting on the plant. In this article, within the framework of the stochastic $H^2/H_{\infty } $-control theory in the presence of noise, we solve the problem of analysis, i.e. finding conditions for the existence of feasible controllers. The results obtained can be used further in the synthesis problem for conditional optimization of a multiplicative stochastic system in the class of feasible dynamic controllers.