Regularizing the singular control law with max(μ,|x1|) or |x1|+μ removes chattering at the origin while preserving iISS, and gives explicit residual error bounds.
Universal integral controllers for minimum-phase nonlinear systems,
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Regularization of non-overshooting quasi-continuous sliding mode control for chattering suppression at equilibrium
Regularizing the singular control law with max(μ,|x1|) or |x1|+μ removes chattering at the origin while preserving iISS, and gives explicit residual error bounds.