Robustness of Nonlinear Predictor Feedback Laws to Time- and State-Dependent Delay Perturbations

TL;DR

This paper investigates the robustness of predictor feedback controllers for nonlinear systems with unknown, time- and state-dependent delay variations, showing stability preservation under small perturbations and rates.

Contribution

It extends stability robustness analysis to nonlinear systems with unknown delay variations, providing conditions for stability preservation under small perturbations.

Findings

Local asymptotic stability is preserved with small delay perturbations and rates.

Global exponential stability for linear systems is robust under small time-varying delays.

Examples include control of a networked DC motor and bilateral teleoperation systems.

Abstract

Much recent progress has been achieved for stabilization of linear and nonlinear systems with input delays that are long and dependent on either time or the plant state---provided the dependence is known. In this paper we consider the delay variations as unknown and study robustness of nominal constant-delay predictor feedbacks under delay variations that depend on time and the state. We show that when the delay perturbation and its rate have sufficiently small magnitude, the local asymptotic stability of the closed-loop system, under the nominal predictor-based design, is preserved. For the special case of linear systems, and under only time-varying delay perturbations, we prove robustness of global exponential stability of the predictor feedback when the delay perturbation and its rate are small in any one of four different metrics. We present two examples, one that is concerned with the control of a DC motor through a network and one of a bilateral teleoperation between two robotic systems.