A hybrid redesign for robust stabilization without unit input

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