This paper presents a theoretical study of decentralized velocity feedback control systems for the reduction of sound transmission through double panels. The system studied consists of two plates which are coupled acoustically by the air in the cavity between them and structurally by four elastic mounts. The geometrical and material properties of the double panel have been chosen so as to approximate a section of an aircraft fuselage skin. The outer panel of the skin (the source panel) is excited by oblique plane waves and the consequent sound power radiated from the inner panel (the radiating panel) is calculated. First, a parametric study of passive sound transmission of double panels with different geometrical and material properties is carried out. Second, active vibration control is implemented using sixteen decentralized direct velocity feedback loops. Performance of such a control system is assessed for four control cases. The first two cases deal with skyhook force actuators with collocated velocity sensors which implement active damping either on the source panel or on the radiating panel. In the third case skyhook actuators and collocated velocity sensors are located on both panels. Finally, an approach using actuators that react between the two panels with collocated relative velocity sensors is considered.