Some problems arising in the implementation of distributed-delay control laws

We study the problems raised by the implementation of a control law including distributed-delay, i.e. a finite integral over the time, such as /spl int//sub 0//sup 1/ x(t-/spl tau/)d/spl tau/. These delays appear in control laws allowing the finite spectrum assignment for time-delay systems, but cannot be exactly implemented on a digital computer. We study some problems that arise when using numerical quadrature methods to implement such control laws.