Passivity based control has several advantages, e.g., robustness and s
implicity. However, the passivity constraint causes performance degrad
ations. Specifically, the degree to which passively controlled absorbe
r systems yield a flat response around the nominal absorber frequency
is limited. An inherent flatness bound is derived using Nevanlinna-Pic
k boundary interpolation theory. For active vibration absorbers, this
limitation cancels, and magnitude response can be made arbitrarily fla
t.