Delay-Robustness of Linear Predictor Feedback Without Restriction on Delay Rate

TL;DR

This paper introduces a straightforward method to determine the maximum delay perturbation magnitude that preserves exponential stability in linear predictor feedback systems, without restrictions on delay rate changes.

Contribution

It provides explicit formulas for delay robustness bounds using small-gain analysis, extending stability guarantees to arbitrary delay variations in linear systems.

Findings

Explicit delay robustness bounds derived

Applicable to measurable and constant delay perturbations

Stability preserved under large, possibly discontinuous delay variations

Abstract

Robustness is established for the predictor feedback for linear time-invariant systems with respect to possibly time-varying perturbations of the input delay, with a constant nominal delay. Prior results have addressed qualitatively constant delay perturbations (robustness of stability in L2 norm of actuator state) and delay perturbations with restricted rate of change (robustness of stability in H1 norm of actuator state). The present work provides simple formulae that allow direct and accurate computation of the least upper bound of the magnitude of the delay perturbation for which exponential stability in supremum norm on the actuator state is preserved. While prior work has employed Lyapunov-Krasovskii functionals constructed via backstepping, the present work employs a particular form of small-gain analysis. Two cases are considered: the case of measurable (possibly discontinuous) perturbations and the case of constant perturbations.