Robustness to time- and state-dependent delay perturbations in networked nonlinear control systems

We consider nonlinear control systems with long, unknown input delays that depend on either time or the plant state, and study robustness of nominal constant-delay predictor feedbacks. 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.