The stochastic optimal control problem is considered for a class of noisy discrete-time linear systems with markovian jumping parameters and quadratic cost. It is assumed that the controller has complete access to the jumping parameters. Using a dynamic programming technique, an optimal control policy is derived, together with an explicit expression for the optimal cost. Besides the intrinsic theoretical interest in its own right, the results derived here may have an important bearing on the study of the partially observable situation (no access to the jumping parameter),inter alia.