Multiplicative stochastic systems: Optimization and analysis

We consider the H ₂/H _∞-optimal control problem for a dynamical system defined by a linear stochastic Itô equation whose drift and diffusion coefficients linearly depend on the state vector, the control signal, and the external disturbance. The optimization is carried out under the a priori requirement of maximum possible damping of the harmful influence of external disturbances on the system operation. We present theorems on the solvability of matrix Riccati differential equations to which the original optimization problem is reduced.