Robustness of nonlinear predictor feedback laws to time- and state-dependent delay perturbations

Much recent progress has been achieved for stabilization of linear andnonlinear systemswith 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 differentmetrics.We present two examples, one that is concernedwith the control of a DCmotor through a network and one of a teleoperation-like system. © 2013 Elsevier Ltd. All rights reserved.