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Nanopositioning is a key enabling technology for nanoscale science and engineering. Many nanopositioning systems employ feedback control to guarantee precise and repeatable positioning. However, achieving the desired performance with conventional feedback systems has remained a challenge. This paper analyzes a novel hybrid control architecture for high-speed nanopositioning, which is based on impulsive control. By impulsively changing the states of the feedback controller, performance objectives can be met that are beyond the limitations of linear feedback. We analyze the stability and performance of impulsive feedback control, and present experimental results in which impulsive control is used for precise motion control in a high-speed scanning-probe microscope.