Fixed‐time stabilization with a prescribed constant settling time by static feedback for delay‐free and input delay systems

Abstract A static nonlinear homogeneous feedback for a fixed‐time stabilization of a linear time‐invariant (LTI) system is designed in such a way that the settling time is assigned exactly to a prescribed constant for all nonzero initial conditions. The constant convergence time is achieved due to a dependence of the feedback gain of the initial state of the system. The robustness of the closed‐loop system with respect to measurement noise and exogenous perturbations is studied using the concept of Input‐to‐State Stability. Both delay‐free and input delay systems are considered. Theoretical results are illustrated by numerical simulations.