Invoking Halanay inequality to conclude on closed-loop stability of a process with input-varying delay1

At the light of a simple tutorial example, this paper discusses the merits of a recently introduced technique to control a class of systems with a delay depending on the past values of the control variables. The convergence proof of the proposed control strategy is obtained by a boundedness analysis of a class of delay differential equation, inspired by the Halanay inequality. The relations of the proposed technique with previous works from the literature on predictor-based controllers are discussed. The treated example is representative of a wide class of systems often observed in process control and distributed parameter systems.