Dominant pole of positive systems with time-delays

Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Frederic Gouaisbaut

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)


This paper is concerned with the dominant pole analysis of asymptotically stable time-delay positive systems (TDPSs). It is known that a TDPS is asymptotically stable if and only if its corresponding delay-free system is asymptotically stable, and this property holds irrespective of the length of delays. However, convergence performance (decay rate) should degrade according to the increase of delays and this intuition motivates us to analyze the dominant pole of TDPSs. As a preliminary result, in this paper, we show that the dominant pole of a TDPS is always real. We also construct a bisection search algorithm for the dominant pole computation, which readily follows from recent results on α-exponential stability of asymptotically stable TDPSs. Then, we next characterize a lower bound of the dominant pole as an explicit function of delays. On the basis of the lower bound characterization, we finally show that the dominant pole of an asymptotically stable TDPS is affected by delays if and only if associated coefficient matrices satisfy eigenvalue-sensitivity condition to be defined in this paper. Moreover, we clarify that the dominant pole goes to zero (from negative side) as time-delay goes to infinity if and only if the coefficient matrices are eigenvalue-sensitive.

Original languageEnglish
Title of host publication2014 European Control Conference, ECC 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9783952426913
Publication statusPublished - Jul 22 2014
Externally publishedYes
Event13th European Control Conference, ECC 2014 - Strasbourg, France
Duration: Jun 24 2014Jun 27 2014

Publication series

Name2014 European Control Conference, ECC 2014


Other13th European Control Conference, ECC 2014

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering


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