This paper presents a theoretical lower bound of the performance index of an on–off damper placed in a state-space system under harmonic disturbance. The bound is obtained by minimizing a single-variable function. The lower bound is a good theoretical benchmark to measure a practical on–off damping controller. The usefulness of the bound is demonstrated through four examples: a vibration isolation system, a quarter-car suspension system, a mass damper system, and a four-mass system. The examples show how the lower bound can be used to improve some conventional controllers.
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