This study is on the structural control experiment for a small scale three-story building structure employing on active mass damper subjected to earthquake loading. $mu$-synthesis controllers, which belong to robust control strategies, were designed and their performance were experimentally verified. Frequency-dependent weighting functions corresponding to disturbance input and controlled output were defined and combined to produce optimal $mu$-synthesis controllers. The experiment result shows 60-70% reduction in RMS responses under the band-limited white noise excitation and 30-45% reduction in peak responses under the scaled earthquake excitations. Good agreement was obtained between the simulations based on the identified mathematical model and experimental results. And the simulations for the system with uncertainties show that the designed controllers are robust within a specified range of uncertainties.