On approximation of distributed-delay control laws

In this note lumped-delay approximations of distributed-delay (DD) control laws are studied. It is shown that approximation problems reported in some recent researches are caused by a brutal combination of a poor approximation accuracy in the high-frequency range (a non-strictly proper approximation of a strictly proper transfer function!) and an excessive sensitivity of the design method to high-frequency additive plant uncertainties. It is also shown that a safe implementation can be achieved by the elimination of either of these two causes. Some remedies toward this end are proposed.