Sufficient conditions for the prediction-based stabilization of linear systems subject to input with input-varying delay

This paper contains a result proving that a predictor feedback controller can effectively yield asymptotic convergence for a class of linear systems with input-dependent delay. The delay is implicit and its model involves past values of the input. It is representative of systems where transport phenomena take place. This situation is frequent in the process industry. The conditions on asymptotic stabilization require the feedback gain to be small. Arguments of proof for this novel result include general Halanay inequalities for delay differential equations and build on recent advances of backstepping techniques for uncertain or varying delay systems.