The purpose of this thesis was to design controllers by using H1 and &sup1 / control strategies in order to suppress the free and forced vibrations of smart structures. The smart structures analyzed in this study were the smart beam and the smart &macr / n. They were aluminum passive structures with surface bonded PZT (Lead-Zirconate-Titanate) patches. The structures were considered in clamped-free con&macr / guration. The &macr / rst part of this study focused on the identi&macr / cation of nominal system models of the smart structures from the experimental data. For the experimentally identi&macr / ed models the robust controllers were designed by using H1 and &sup1 / -synthesis strategies. In the second part, the controller implementation was carried out for the suppression of free and forced vibrations of the smart structures. Within the framework of this study, a Smart Structures Laboratory was established in the Aerospace Engineering Department of METU. The controller implementations were carried out by considering two di&reg / erent experimental set-ups. In the &macr / rst set-up the controller designs were based on the strain measurements. In the second approach, the displacement measurements, which were acquired through laser displacement sensor, were considered in the controller design. The &macr / rst two &deg / exural modes of the smart beam were successfully controlled by using H1 method. The vibrations of the &macr / rst two &deg / exural and &macr / rst torsional modes of the smart &macr / n were suppressed through the &sup1 / -synthesis. Satisfactory attenuation levels were achieved for both strain measurement and displacement measurement applications.