Limitations of a class of stabilization methods for delay systems

In this note, we investigate limitations of certain stabilization methods f or time-delay systems. The class of methods under consideration implements the control law through a Volterra integral equation of the second kind. Us ing as an example the pole placement approach of Manitius and Olbrot, we il lustrate how instability of the difference part of the control law leads to instability in the closed-loop system, in case the implementation is done via numerical quadrature, The outcome of our analysis provides computable l imitations to stability and a maximum allowable size of the (input) delay.