A forwarding-based approach for the stabilization of linear systems in the presence of delayed nonlinear actuators

In this paper, we revisit the forwarding approach for the input-to-states stabilization of linear systems subject to external perturbations, input nonlinearities (e.g. saturation and backlash functions), and different input delays. For this problem, we propose a Lyapunov functional analysis in the original coordinates certifying input-to-states stability of the origin with any desired type of convergence (asymptotic, finite-time, fixed-time, etc). At the end, we present some numerical simulations to show the effectiveness of our method and to show that in the linear case we recover the well-known backstepping methodology for delay compensation.