Unified framework for graphical and non-graphical stability conditions

Develop a framework that generalizes over graphical stability conditions based on the Davis–Wielandt shell, numerical range, and x–z graph together with non-graphical stability conditions such as the unified framework and IQC-based methods.

Background

The paper develops frequency-domain quadratic constraints (FQCs) as a framework that recovers several existing stability conditions for multi-converter power systems. These include graphical conditions based on geometric representations such as the Davis–Wielandt shell, numerical range, and x–z graph, as well as non-graphical gain-, phase-, and IQC-based conditions.

The authors explicitly identify it as unresolved whether a single framework can generalize across both classes of stability conditions. This problem concerns unification of the theoretical descriptions and their associated decentralized verification requirements, rather than merely applying the FQC framework proposed in the paper.