Distributed parameter models accurately predict vibration and noise in many manufacturing, space, HVAC, robotics, transportation, and power transmission systems. This book presents recent advances in the application of Lyapunov's method to the control of distributed vibration and noise. The book focuses on the development of adaptive, output feedback controllers that provide asymptotic stabilization using few sensors and actuators, compensate for actuator dynamics, and learn system parameters. Distributed parameter modeling, visual feedback control using high speed video, setpoint regulation for systems with rigid body modes, and active isolation of bounded disturbances are also presented.