Fixed-time Stabilization with a Prescribed Constant Settling Time by Static Feedback for Delay-Free and Input Delay Systems

TL;DR

This paper introduces a static nonlinear feedback control method that guarantees a fixed, prescribed settling time for linear systems, ensuring robustness against disturbances and applicable to systems with or without input delays.

Contribution

It proposes a novel static feedback design that precisely assigns the settling time for LTI systems, extending to systems with input delays and analyzing robustness using ISS.

Findings

Achieves exact fixed-time stabilization with prescribed settling time.

Demonstrates robustness against measurement noise and external disturbances.

Validates theoretical results through numerical simulations.

Abstract

A static non-linear 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 noises and exogenous perturbations is studied using the concept of Input-to-State Stability (ISS). Both delay-free and input delay systems are studied. Theoretical results are illustrated by numerical simulations.