Controller design of systems with multiplicative noise

General linear continuous stochastic systems are considered with multiplicative noise in the control and state channels and stabilizing optimal inputs are synthesized for both time-varying and time-invariant situations. In the nonstationary case, a set of nonlinear matrix differential equations has to be solved. In the stationary problem, a set of nonlinear matrix algebraic equations provides the solution. The separation principle is not valid and both the state filtering and the control synthesis problem should be treated simultaneously.