The purpose of this work is to analyze the optimality of pulsed actuations of leaky resonators when the ratio between the resonator and sampling frequencies is irrational. This is the case when the actuation system and resonator are non-synchronized or uncoupled. It will be proven that any bounded pulsed actuation of a leaky resonator cannot be optimal for maximizing the energy of a leaky resonator from a certain time onwards. Therefore sustained optimal energy transfer to a resonator will require a certain degree of coupling between the actuation system and the resonator, allowing their respective frequencies to have a rational proportionality

Peer Reviewed