Abstract—The stability of a switching system arising from the use of a discontinuous feedback to stabilize a second-order integrator is analyzed. This is the limiting case of the feedback in the form of nested saturation functions considered previously, where the external saturation function or sigmoid is replaced by the discontinuous function sgn(x). Such a feedback involves a bounded control resource and ensures constraints on the phase velocity of approaching an equilibrium, which is especially important under large initial deviations. A Lyapunov function for the closed-loop system is proposed, and the global asymptotic stability of the origin is proven using this function and the results of Filippov’s theory, provided that the switching curve is a continuously differentiable and monotonic function passing through zero. The global stability of the origin is preserved when relaxing the smoothness requirement for the entire switching function to its continuous differentiability everywhere except for a finite set of points where the derivative does not exist, but continuity holds. In the case of a discontinuous switching curve, the origin is shown to be a sewn center according to Filippov’s classification. In this case, the closed-loop system has a semi-stable cycle enclosing a set of discontinuity points on the switching curve. As numerical examples, the level line of the Lyapunov function and phase trajectories on the plane are constructed for different types of switching curves.