Dominant pole of positive systems with time-delays

Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier, Frederic Gouaisbaut

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

6 被引用数 (Scopus)

抄録

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.

本文言語英語
ホスト出版物のタイトル2014 European Control Conference, ECC 2014
出版社Institute of Electrical and Electronics Engineers Inc.
ページ79-84
ページ数6
ISBN(電子版)9783952426913
DOI
出版ステータス出版済み - 7 22 2014
外部発表はい
イベント13th European Control Conference, ECC 2014 - Strasbourg, フランス
継続期間: 6 24 20146 27 2014

出版物シリーズ

名前2014 European Control Conference, ECC 2014

その他

その他13th European Control Conference, ECC 2014
Countryフランス
CityStrasbourg
Period6/24/146/27/14

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

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