On the fixed-time stabilization of input delay systems using act-and-wait control

We address the state feedback stabilization of linear systems with input delay using the so-called act-and-wait control strategy. The latter approach induces an analysis of the closed-loop stability based on a finite-dimensional monodromy operator, and rendering this matrix nilpotent results in fixed-time stability. We show that any controllable planar system can be stabilized in a fixed time, and the constructive proof reveals that always two isolated solutions for the corresponding controller gain co-exist. Next, for the fixed-time stabilization of general linear systems, we present both a novel numerical approach for the computation of the controller gain, and an analytic approach relying on incorporating a predictor and an appropriately defined feedback transformation in the control scheme. Several illustrations complete the presentation.