Strong stabilization is defined as finding a stable controller that stabilizes the feedback system for a given plant. This study addresses the strong stabilization of a robotic system called the “acrobot”, which is a two-linked underactuated planar robot system. The linearized system is fourth-order, with two poles and one zero in the right half-plane. In this thesis, stable second-order controllers designed with different methods have been investigated for this system. The sta-bility margins are analyzed with respect to various free parameters. In addition, the time-domain transient response analysis is illustrated through simulations. Furthermore, the effects of nonlinearities are studied by estimating the region of attraction for each linear controller considered.