TY - GEN

T1 - Dominant pole of positive systems with time-delays

AU - Ebihara, Yoshio

AU - Peaucelle, Dimitri

AU - Arzelier, Denis

AU - Gouaisbaut, Frederic

PY - 2014/7/22

Y1 - 2014/7/22

N2 - 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.

AB - 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.

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U2 - 10.1109/ECC.2014.6862165

DO - 10.1109/ECC.2014.6862165

M3 - Conference contribution

AN - SCOPUS:84911493427

T3 - 2014 European Control Conference, ECC 2014

SP - 79

EP - 84

BT - 2014 European Control Conference, ECC 2014

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 13th European Control Conference, ECC 2014

Y2 - 24 June 2014 through 27 June 2014

ER -