We present a numerical evaluation of the potential improvements in sei
smic disturbance rejection to be obtained by using active variable dam
ping control in a structure. Using the responses to seismic excitation
of an optimally controlled variable structure and of a minimax-optima
l designed fixed structure, we obtain an upper bound on the achievable
performance and a lower bound on the acceptable performance of a cont
rol system for a variable-damping structure. Both of these bounds are
relative to an energy-function criterion. Our numerical experiments le
ad to the following conclusions: (i) The gap between the upper and low
er bounds is rather small, which makes designing a feedback law, that
results in performance superior to that of a minimax-optimal designed
structure, very difficult. The best choice for a feedback law appears
to be continuous moving horizon control, whose implementation requires
ground motion prediction up to 0.2 sec ahead, possibly using sensors
located a small distance away from the site. (ii) A minimax-optimal de
signed structure gives very good seismic disturbance suppression, not
only for the earthquakes used in its design, but also for other earthq
uakes of similar intensity. Controlled variable structures are likely
to offer advantages when earthquakes are moderate to severe, particula
rly at sites, such as landfills and dry lake beds, where resonances ca
n be expected, but the resonance frequency cannot be estimated in adva
nce.