This paper provides new results for a newly introduced control scheme, Sign Inverting Control (SIC), for linear time-invariant multiple time delay systems (LTI-MTDS). SIC suggests the inversion of the control polarity for delayed systems and it functions with one single requirement that the union of the control schemes provides a larger operating region in the domain of the delays than each of its components does. To meet this need, we propose a new method to characterize the potential stability-switching hypersurfaces for SIC applied systems. The acquisition of these hypersurfaces is a prerequisite for the description of the overall stability map. The new results in this paper reveal the relationship between the hypersurfaces of the SIC applied system and the original nominal system. As a result, the procurement of the hypersurfaces and stability map of the SIC applied system has been facilitated. Several illustrative example case studies are presented.

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