Compensation of time-varying input delay for nonlinear systems

We consider general nonlinear systems with time varying input delay for which we design a predictor-based feedback controller. Under the assumptions of forward completeness of the open-loop system and the existence of a (possibly time-varying) stabilizing controller, in the absence of the input delay, our controller achieves global asymptotic stability in the presence of a time-varying input delay. We prove asymptotic stability based on a backstepping transformation which enables us to construct a Lyapunov functional. Our design is illustrated by a numerical example of a second order system.