Implementation of delayed output feedback for linear systems with multiple input delays

This study is concerned with the safe implementation of delayed output feedback (DOF) for linear systems with multiple input delays. It is observed that the numerical implementation of the distributed delay terms involved in the DOF controller may lead to instability of the closed-loop system. To solve this problem, a generalised low-pass filter (LPF) is introduced into the control loop. It is shown that the stability of the closed-loop system can be maintained if the numerical integration is sufficiently precise. An augmented system is then constructed to design the LPF by applying the traditional pole assignment algorithm for linear systems without delay. Two illustrative examples are worked out to show the effectiveness of the proposed approach.