TY - JOUR
T1 - Asymptotic stability of a repairable system with imperfect switching mechanism
AU - Xu, Houbao
AU - Guo, Weihua
AU - Yu, Jingyuan
AU - Zhu, Guangtian
PY - 2005/4/20
Y1 - 2005/4/20
N2 - This paper studies the asymptotic stability of a repairable system with repair time of failed system that follows arbitrary distribution. We show that the system operator generates a positive C0-semigroup of contraction in a Banach space, therefore there exists a unique, nonnegative, and time-dependant solution. By analyzing the spectrum of system operator, we deduce that all spectra lie in the left half-plane and 0 is the unique spectral point on imaginary axis. As a result, the time-dependant solution converges to the eigenvector of system operator corresponding to eigenvalue 0.
AB - This paper studies the asymptotic stability of a repairable system with repair time of failed system that follows arbitrary distribution. We show that the system operator generates a positive C0-semigroup of contraction in a Banach space, therefore there exists a unique, nonnegative, and time-dependant solution. By analyzing the spectrum of system operator, we deduce that all spectra lie in the left half-plane and 0 is the unique spectral point on imaginary axis. As a result, the time-dependant solution converges to the eigenvector of system operator corresponding to eigenvalue 0.
UR - http://www.scopus.com/inward/record.url?scp=24944572953&partnerID=8YFLogxK
U2 - 10.1155/IJMMS.2005.631
DO - 10.1155/IJMMS.2005.631
M3 - Article
AN - SCOPUS:24944572953
SN - 0161-1712
VL - 2005
SP - 631
EP - 643
JO - International Journal of Mathematics and Mathematical Sciences
JF - International Journal of Mathematics and Mathematical Sciences
IS - 4
ER -