Stochastic $H_2/H_\infty$-control for a dynamical system with internal noises multiplicative with respect to state, control, and external disturbance

We consider an optimal control problem for a dynamical system under the influence of disturbances of both deterministic and stochastic nature. The system is defined on a finite time interval, and its diffusion coefficient depends on the control signal. The controller in the feedback circuit is assumed to be static, nonstationary, linear in the state vector, and satisfying the condition $\|L\|_\infty<\gamma$ that bounds the norm of operator $L\colon v\mapsto z$ for the transition of external disturbance to the controllable output signal. Solving the optimization $H_2/H_\infty$-control problem, we get three matrix functions satisfying a system of two differential equations of Riccati type and one matrix algebraic equation. In the special case of a stochastic system whose diffusion coefficient does not depend on the control signal, the system is reduced to two related Riccati equations.