Determine suitable homotopy paths for black-box device admittances

Determine a proper homotopy path for each type of device represented only by experimentally obtained or black-box admittance spectra, starting from a definitely stable configuration and preserving the validity of the multiplier-based stability conditions throughout the homotopy.

Background

The proposed plug-and-play stability certificates rely on a homotopy connecting the actual device configuration to a configuration known to be stable. For white-box models, the paper illustrates this by reducing controller gains to zero, but that operation is unavailable when only measured or vendor-supplied admittance spectra are available.

The paper proposes replacing the device with a fictitious passive element and continuously interpolating between the passive admittance and the device admittance. However, the interpolation is not unique, and the appropriate path may depend on the device and system configuration. Selecting a path that preserves the required non-singularity and positive-definiteness conditions is therefore left unresolved.