Linear Output-Feedback Control of Stochastic Linear Systems with State- and Control-dependent Disturbances

The stochastic regulation problem for linear systems with state- and control-dependent noise and a noisy linear output equation is considered. The optimal, quadratic cost, output-feedback control law in a class of linear controllers is found. The result represent an extension to the incomplete information case of the class of optimal control problems just considered in the 70´s by McLane. As a result, the optimal control law result to be similar to the Linear-Quadratic- Gaussian (LQG) regulator, but a new non-negative matrix (associated to the quadratic-variation of the control-dependent noise) must to be added to the output noise covariance.