Topological theory of 0/0 ambiguities in robust control

Allowing some uncertain parameters in the numerator and denominator polynomials of the loop function of a feedback system can result in 0/0 ambiguities at some uncertain points. This in turn could create discrepancies between the stability margins computed from the "value set" approach and the "Horowitz template" approach. In addition, in case of some "essential" ambiguities, the singularity set of the Nyquist map-crucially related to continuity of the margins-is structurally unstable and nearly impossible to compute.