The problem of determining the linear feedback control of the instantaneous system output which minimizes a quadratic performance measure for a linear system with state and control-dependent noise is solved in this paper. Both the finite and infinite terminal time versions of this problem are treated. For the latter case, a sufficient condition for the existence of an optimal control is obtained. For the finite terminal time problem, it is shown that a two-point boundary value problem must be solved to realize the optimal control. For the infinite terminal time case, two non-linear matrix equations must be solved to realize the optimal control. Some discussion on the numerical methods used by the author to solve these equations is included in the paper.