We propose a control law for stabilization of a bar tethered to two aerial vehicles, and provide conditions on the control law's gains that guarantee exponential stability of the equilibrium. Given the proposed control law, we analyze the stability of the equilibrium for two cases, specifically, for a bar of known and unknown mass. We provide lower bounds on the attitude gains of the UAVs' attitude inner loop that guarantee exponential stability of the equilibrium. We also include an integral action term in the control law, so as to compensate for battery drainage and model mismatches, and we provide a lower bound on the integral gain that guarantees stability of the equilibrium. We present an experiment that demonstrates the stabilization and that validates the robustness of the proposed control law.