Loss of structurally stable regulation implies loss of stability

We refer to systems violating the conditions for structurally stable regulation as critical. At least one of the following must fail at a critical system: asymptotic rejection of the exogenous system, stabilization of the closed-loop system, or structural stability. This has not been explicitly addressed. We show that any structurally stable regulator is necessarily destabilizing when applied to a critical system, that destabilization is linked to structural stability, and we characterize the resulting unstable poles.