Before revision:  We also prove the need for a physical damping term in parallel to the series elastic element to ensure two-port passivity , even when a virtual coupler is present. Finally, we validate our theoretical results through numerical simulations and by reproducing one-port passivity results as special cases of our results that correspond to appropriate one-port terminations .
After revision:  We also prove the need for a physical damping term in parallel to the series elastic element to ensure two-port passivity of the system. The additional dissipative elements in the physical filter and the virtual coupler enable the system to render virtual stiffness values higher than that can be rendered using a pure SEA. Our results extend earlier studies on coupled stability by presenting the necessary and sufficient conditions for all passive terminations. We validate our results through a set of physical experiments and systematic numerical simulations .