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.