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With the rise of network science old topics in ecology and economics areresurfacing. One such topic is structural stability (often referred to asqualitative stability or sign stability). A system is deemed structurallystable if the system remains stable for all possible parameter variations solong as the parameters do not change sign. This type of stability analysis isappealing when studying real systems as the underlying stability result onlyrequires the scientist or engineer to know the sign of the parameters in themodel and not the specific values. The necessary and sufficient conditions forqualitative stability however are opaque. In order to shed light on thoseconditions root locus analysis is employed. This technique allows us toillustrate the necessary conditions for qualitative stability.

Sign Stability via Root Locus Analysis