LIMITATIONS OF DELAYED STATE FEEDBACK: A NUMERICAL STUDY

Abstract

Stabilization of a class of linear time-delay systems can be achieved by a numerical procedure, called the continuous pole placement method [Michiels et al., 2000]. This method can be seen as an extension of the classical pole placement algorithm for ordinary differential equations to a class of delay differential equations. In [Michiels et al., 2000] it was applied to the stabilization of a linear time-invariant system with an input delay using static state feedback. In this paper we study the limitations of such delayed state feedback laws. More precisely we completely characterize the class of stabilizable plants in the 2D-case. For that purpose we make use of numerical continuation techniques. The use of delayed state feedback in various control applications and the effect of its limitations are briefly discussed.