Stability analysis of time-delay systems in the parametric space

Abstract

This paper presents a novel method for stability analysis of a wide class of linear, time-delay systems (TDS), including retarded, incommensurate and distributed delays. The proposed method is based on frequency domain analysis and application of Rouché’s theorem. Given a parametrized TDS and an arbitrary parametric point, the proposed method is capable of identifying the surrounding region in the parametric space for which the number of unstable poles remains invariant. First, a procedure for investigating stability along a line is developed. Then, the results are extended by application of Hölder’s inequality to investigate stability within a region. The proposed method is uniformly applicable to parameters of different types (simple delays, distributed delay limits, time constants, etc.), as illustrated by examples.