A hybrid redesign for robust stabilization without unit input

We propose a redesign strategy to avoid an arbitrary value of the input signal. With a hybrid architecture based on a switching logic with two modes we obtain robust global asymptotic stability and ensure that the input never takes the unwanted value, while preserving the nominal closed-loop behaviour in a neighbourhood of the origin. In the case where the minimization problem is too computationally expensive, we provide a simpler, albeit more conservative, way to determine the scaling factor. We then present a nonlinear generalization to a fairly general class of input-affine nonlinear systems. Numerical examples are used to illustrate the theoretical results.