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Control design of active dynamic vibration absorber based on homogeneous control Lyapunov functions

Active dynamic vibration absorbers are widely known as vibration controllers exhibiting good performance for disturbance signal with various frequencies. Generally, LQ control is used in active dynamic vibration absorber. In this paper, we show that nonlinear control laws supply vibration control performance higher than the LQ control laws by designing homogeneous CLF control laws. The effectiveness of our controllers is confirmed by the analysis of transient and steady-state frequency responses with numerical simulation.