A semistate approach to feedback stabilization of neutral delay systems

Abstract

In this paper we consider derivative feedback in a semistate framework for the problem of stabilizing the neutral root chains for a class of neutral delay-differential equations where the difference operator (orD-operator) is unstable. Recent work has shown that such systems cannot be stabilized by state feedback alone[3], [13], [16]. In addition, we consider the problem of using derivative feedback to eliminate all neutral root chains entirely, thus turning the closed loop system into a retarded delay system. By representing neutral delay-differential systems as semistate systems over a polynomial ring of delay operators, both of the above problems are shown to be reducible to the following question: Given matricesD,B over a commutative ringR, when does there exist a matrixM also overR such thatD+BM isR-unimodular? In the case of commensurable point delays our results are applications of some recent results on the simultaneous stabilization problem [19], and we give a constructive procedure for computing the required feedback law. In the case of noncommensurable delays we give a sufficient condition for the existence of suitable feedback for the above problems.