On distributed delay in linear control laws - part II: rational implementations inspired from the δ-operator

This note proposes rational implementations for distributed delay in linear control laws. The main benefit of doing so is the easy implementation of rational transfer functions. The proposed approach was inspired from the δ-operator. The resulting rational implementation has an elegant structure of chained low-pass filters. The stability of each node can be guaranteed by the choice of the number N of the nodes. The stability of the closed-loop system can also be guaranteed since the H^∞-norm of the implementation error approaches 0 when N goes to ∞. Moreover, the steady-state performance of the system is retained without the need to change the control structure.