It has recently been recognized that the non-normality of the dynamical operator obtained by the linearization of the equations of motion about the strongly sheared background flow plays a central role in the dynamics of both fully developed turbulence and laminar/turbulent transition. This advance has led to the development of a deterministic theory for the role of coherent structures in shear turbulence as well as a stochastic theory for the maintenance of the turbulent state. In this work the theory of stochastically forced non-normal dynamical systems is extended to explore the possibility of controlling the transition process and of suppressing fully developed shear turbulence. Modeling turbulence as a stochastically forced non-normal dynamical system allows a great variety of control strategies to be explored and their physical mechanism understood. Two distinct active control mechanisms have been found to produce suppression of turbulent energy by up to 70%. A physical explanation of these effective control mechanisms is given and possible applications are discussed