Delay-dependent stability analysis by using delay-independent integral evaluation

Qi Xu, G. Stépán, Zaihua Wang

Research output: Contribution to journalArticle

27 Citations (Scopus)


For the stability analysis of time-delay systems, the available methods usually require the exact evaluation of some quantities. The definite integral stability method, originated from the Argument Principle or the Cauchy Theorem, is effective because it only requires a rough estimation of the testing integral over a finite interval to judge stability. However, no general rule is given in the literature for properly choosing the upper limit of the testing integral. In this paper, two simple algorithms are presented for finding the parameter-dependent critical upper limit and a parameter-independent upper limit without any restriction on the number of time delays. These results improve and complete the definite integral stability method. As illustrated by the numerical examples, the proposed algorithms work effectively and accurately.

Original languageEnglish
Pages (from-to)153-157
Number of pages5
Publication statusPublished - Aug 1 2016


  • Definite integral
  • Delay-dependent
  • Delay-independent
  • Neutral
  • Retarded
  • Stability
  • Time delay

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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