In the first part of the paper linear-quadratic control problem under indenendent random perturbations is considered. Under a controllability assumption it is shown that every linear admissible feedback control stabilizes the control system.

Using this fact,a procedure to construct a monotone decreasing sequence of quadratic forms which converges to the optimal value of the control problem is discussed. Similar results for the linear-quadratic control problem under jump Markov perturbations are also obtained. In the last part of the paper, some necessary conditions for the stabilizability of a class of linear discrete-time control systems with independent random perturbations are derived