Stability is a challenging issue when controlling haptic interaction systems because unstable behavior may injure human operators or deteriorate the realism of the provided cues. Based on the passivity condition for sampled-data haptic systems, we propose a novel energy-bounding algorithm to ensure robustly stable haptic interactions. The proposed algorithm limits the energy generated by a sample-and-hold operator within the energy consumable by the effective damping elements in the haptic system. The algorithm also ensures that the VE and controller are passive. This guarantees robustly stable haptic interactions, regardless of the sampling frequency and its variations, but compromises the displayable impedance range of the VE. Simulations and experiments using a commercial haptic device are used to demonstrate the effectiveness of the proposed algorithm.