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This book presents recent advances in the application of Lyapunov's method for distributed parameter systems to the control of vibration and noise. The material is appropriate for graduate and advanced undergraduate students as well as academic and industrial researchers in engineering and mathematics. The book uses detailed examples to introduce modeling, control theory, and mechatronic implementation for distributed vibration and noise applications. Adaptive, output feedback controllers are shown to asymptotically stabilize distributed vibration and noise and to learn system parameters. Visual feedback control using high speed video and setpoint regulation for systems with rigid body modes are presented. The book provides readers with the tools to model distributed vibration and noise systems, design model-based controllers that guarantee stability and robustness, and implement the controllers with the appropriate sensing, actuation, and control hardware and software.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.