On the approximation of distributed-delay control laws

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