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Much recent progress has been achieved for stabilization of linear andnonlinear systems with input delays that are long and dependent on either timeor the plant state---provided the dependence is known. In this paper weconsider the delay variations as unknown and study robustness of nominalconstant-delay predictor feedbacks under delay variations that depend on timeand the state. We show that when the delay perturbation and its rate havesufficiently small magnitude, the local asymptotic stability of the closed-loopsystem, under the nominal predictor-based design, is preserved. For the specialcase of linear systems, and under only time-varying delay perturbations, weprove robustness of global exponential stability of the predictor feedback whenthe delay perturbation and its rate are small in any one of four differentmetrics. We present two examples, one that is concerned with the control of aDC motor through a network and one of a bilateral teleoperation between tworobotic systems.

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