A Lyapunov-based construction of a predefined-time stabilizing function (a function that stabilizes a system in fixed-time with settling time as function of the controller parameters) for scalar systems is considered in this paper. The constructed function involves the inverse incomplete gamma function, causing this function to be semi-global, i.e., the domain of definition of the function can be made as large as wanted with an appropriate parameter selection. Finally, the constructed function is used to design predefined-time stabilizing controllers which are robust against vanishing and non-vanishing perturbations.
