Limitations of a class of stabilization methods for delay systems

We investigate limitations of certain stabilization methods for time-delay systems. The class of methods under consideration implements the control law through a Volterra integral equation of the second kind. Using as an example the pole placement approach of Manitius and Olbrot (1979), we illustrate how instability of the difference part of the control law leads to instability in the closed-loop system, in the case that implementation is done via numerical quadrature. The outcome of our analysis provides computable limitations to stability and a maximum allowable size of the (input) delay.