期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2005
卷号：2005
DOI：10.1155/IJMMS.2005.631
出版社：Hindawi Publishing Corporation
摘要：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.
