Implementation of a distributed control law for a class of systems with delay

Abstract

The use of distributed delays in the control law of time-delay systems has been proposed by several authors. The implementation of such controllers is not trivial, and recent publication shown that replacing the distributed delay operator by an approximation computed through pointwise delay operators was unsafe with respect to the stability of the systen1. In this paper the use of digital controller is addressed, for the control of systems with an input delay. Practically, this means replacing an integral by a recurrent system. The first approach was to use a method of numerical approximation of an integral to build the recurrence law. In this paper it is shown that a such controller, built with the Simpson method, leads to an unstable closed-loop system. A second approach leads to the construction of a control law which realizes a sampled pole assignment, in the same way as the distributed control law realizes a pole assignment in continuous time.