A locally synthesized controller (LSC) is one that uses a local feedback signal in a noise or vibration field (VF) to synthesize the actuation signal. The global damping of a VF by available LSCs requires sensor-actuator collocation. This study presents a LSC for the global damping of a VF without requiring sensor-actuator collocation, which is important to noise control applications where a sensor may be placed away from an actuator to avoid the near field effects. It is proven that the LSC damps the entire VF instead of just a local feedback loop. This is different from other LSCs that may control local feedback loops without damping the VFs. A decentralized control law is presented here to extend the LSC to a decentralized damping system using multiple actuators.