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. This problem was first addressed in the early 1970s and solved, in the complete information case, by Wonham. In this paper we give the solution of the problem in the incomplete information case, that is, for a linear output equation corrupted by Gaussian noise. Moreover, a different method is used here, giving the solution in a more direct way even in the complete information case. (c) 2007 Published by Elsevier Ltd.