An Asymmetric Instability Threshold for Fixed-Gain Sliding Mode Control with Discontinuous Switching Under Power-Law Contact Stiffness Mismatch

This revised preprint studies stiffness-coefficient mismatch in fixed-gain sliding-mode control with discontinuous switching for a power-law contact model under actuator saturation. The original closed-form local sliding-existence threshold is retained, but its global interpretation is corrected and extended. The revised analysis shows that actuator saturation can create a stable remote equilibrium before the local positive-mismatch threshold is reached, producing a basin-dependent coexistence region. It also clarifies that negative stiffness mismatch has a finite persistence boundary rather than being threshold-free. The revision therefore distinguishes three effects that should not be conflated: local loss of ideal sliding, saturation-induced multistability, and the persistence of a lower stable branch under negative mismatch. Main results include: the local sliding-existence threshold under stiffness mismatch; the earlier positive-mismatch saturation threshold; a coexistence interval containing target sliding, a switched saddle, and a saturation-locked attractor; basin dependence below the conventional positive threshold; a finite negative-mismatch persistence boundary; a corrected interpretation of the asymmetry between stiffness overestimation and underestimation. This Version 2 supersedes the global-convergence interpretation of the original version while preserving the original local threshold result and numerical evidence. A detailed revision note is included in the deposit.