This paper presents a control approach for HVDC interconnections that provides damping of frequency oscillations in asynchronous ac grids by introducing a virtual friction for coupling their inertial dynamics. The HVDC interconnection is modelled by using the concept of common and differential power flow, allowing for independent control of the dc voltage and the net power transfer between HVDC terminals, respectively. The proposed controller introduces a damping effect in the differential power flow which is equivalent to a mechanical friction between the generators connected to the ac grids at the two terminals. This virtual friction-based damping can effectively attenuate poorly damped frequency oscillations that can be observed where the HVDC interconnection is interfaced to either of the ac grids without relying on fast communication between the converter terminals. The impact of the proposed control technique on the stability and damping of two interconnected power systems is first analysed by using a simplified model. Then, the sensitivity to the frequency and damping of the oscillation modes appearing in the ac grid frequencies, as well as the effect of the dc line resistance on the oscillation damping are evaluated. Finally, the control system performance is experimentally validated on a scaled laboratory setup.