A synopsis of the non-invertible, two-dimensional, border-collision normal form with applications to power converters

The model correctly derives the trace–determinant stability strip for L^{p-1}R cycles, the ±1 multiplier boundaries, the collapse curve δ_R = −1/δ_L^{p−1}, and the p=2 boundary lines. However, it incorrectly claims that admissibility holds throughout the whole preimage of the Schur strip and that the resonance tongue is bounded “precisely” by the ±1 curves. The paper explicitly shows additional admissibility boundaries (border-collisions) that truncate the tongue from above, so stability inequalities alone do not guarantee admissibility everywhere in the strip. See the statements and figures on the strip (−det(M_p)−1 < tr(M_p) < det(M_p)+1) and its ±1 edges, and on the collapse curve (δ_R = −1/δ_L^{p−1}), together with the explicit LR p=2 lines and the presence of upper border-collision caps that bound admissibility (e.g., Fig. 6 narrative). These directly contradict the model’s “bounded precisely by ±1” claim and its equivalence of admissibility with the Schur strip.