TITLE:
Asymptotic Stability of the Dynamic Solution of an N-Unit Series System with Finite Number of Vacations
AUTHORS:
Abdugeni Osman, Abdukerim Haji, Askar Ablimit
KEYWORDS:
N-Unit Series System, C0-Semigroup, Irreducibility, Asymptotic Stability
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.11,
November
13,
2018
ABSTRACT: We investigate an N-unit series system with finite
number of vacations. By analyzing the spectral distribution of the system
operator and taking into account the irreducibility of the semigroup generated
by the system operator we prove that the dynamic solution converges strongly to
the steady state solution. Thus we obtain
asymptotic stability of the dynamic solution of the system.