A key challenge to enable the interoperability of a Multi-Vendor-Multi-Terminal (MVMT) HVDC network is to assess the stability without requiring open sharing of the vendor Intellectual Property (IP) relating to control functions. An analytical criterion is therefore proposed as a first step of this assessment. The criterion is indexed by the margin against loss-ofequilibrium for a MVMT-HVDC network with terminal behaviour of connected converters. Based on a classical control architecture, a static analytical model is established, including relevant parameters within the DC network, its topology and operation. By linearizing the system at 0 Hz, the principle of assessing the singularity of the matrix of extended conductance is proposed and proved with the theorem of implicit function and principle of analytic continuation. Two types of scaler index are proposed and then normalized to indicate the margin against loss-of-equilibrium. The effectiveness of the indices is verified and analysed with simulations in the environments of both Matlab/Simulink and RTDS with pseudo-steady-state and detailed Electro-Magnetic Transient (EMT) modelling, respectively. This approach attempts to represent one MVMT control scheme to support practical specification, testing and demonstration of the first multi-vendor multi-terminal HVDC control system outside of China.