Imaginary characteristic roots of neutral systems with commensurate delays

Abstract

This paper concentrates on stability analysis of neutral linear time-invariant (LTI) delay systems with multiple commensurate time-delays. A new numerical procedure is offered for the determination of purely imaginary characteristic roots of neutral delay systems, which plays a crucial role in assessing the system stability. Based on simple linear algebra it is shown that the imaginary characteristic roots of such a system can be found by calculating the generalized eigenvalues of an associated matrix pair. If the system is of retarded type we just need to determine the eigenvalues of a single matrix. The results extend previously known work on neutral delay systems subject to a single delay for neutral systems subject to multiple commensurate delays. In the light of the main result of this paper we present a new method to determine the largest first time-delay interval for which a neutral delay system preserves its stability. The paper is closed by showing numerical examples that illustrate the applicability and effectiveness of the proposed method.