Computation of imaginary axis eigenvalues and critical parameters for neutral time delay systems

Abstract

In this paper, a procedure for the computation of the Lyapunov matrix of neutral type systems, with delays multiple of a basic one, is recalled: It consists in solving a boundary value problem for a delay free system of matrix equations. The important property that the elements of the spectrum of the delay system that are symmetric with respect to the imaginary axis belong to the spectrum of the delay free system is also established. This property is exploited for the determination of the critical values of the time delay system. © 2012 Springer-Verlag GmbH Berlin Heidelberg.