Stability analysis for a class of distributed delay systems with constant coefficients by using a frequency‐sweeping approach

Abstract

This study focuses on the stability property of a class of distributed delay systems with constant coefficients. More precisely, the authors will discuss deeper the stability analysis with respect to the delay parameter. The authors' approach will allow to give new insights in solving the so-called complete stability problem. There are three technical issues need to be studied: First, the detection of the critical zero roots (CZRs); second, the analysis of the asymptotic behaviour of such CZRs; third, the asymptotic behaviour analysis of the critical imaginary roots (CIRs) with respect to the infinitely many critical delays. They extended their recently-established frequency-sweeping approach, with which these technical issues can be effectively solved. Based on these results, a procedure was proposed, with which the complete stability analysis of such systems was accomplished systematically. Moreover, the procedure represents a unified approach: Most of the steps required by the complete stability problem may be fulfilled through observing the frequency-sweeping curves. Finally, some examples illustrate the effectiveness and advantages of the approach.