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In the past, manipulators, machine tools, measurement and many other systems were designed with rigid structures and operated at relatively low speeds. With an increasing demand for fuel efficiency, smaller actuators, and speed, lighter weight materials are now often used in the construction of systems, making them more flexible. Flexible structures are also prevalent in space systems where lightweight materials are necessitated for fuel efficiency when carrying the structures into space. Achieving high-performance control of flexible structures is a difficult task, but one that is now critical to the success of many important applications, ranging from the shuttle remote manipulator system, satellites, robot manipulators, gantry cranes, disk drives, to atomic force microscopes. The unwanted vibration that results from maneuvering a flexible structure often dictates limiting factors in the performance of the system.