Asymptotic stability of a repairable system with imperfect switching mechanism | Zendy

Houbao Xu | Zendy; Guo Wei-hua | Zendy; Jingyuan Yu | Zendy; Guangtian Zhu | Zendy

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Asymptotic stability of a repairable system with imperfect switching mechanism

Author(s) -

Houbao Xu,

Guo Wei-hua,

Jingyuan Yu,

Guangtian Zhu

Publication year - 2005

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/ijmms.2005.631

Subject(s) - mathematics , eigenvalues and eigenvectors , exponential stability , contraction (grammar) , operator (biology) , spectrum (functional analysis) , complex plane , banach space , imperfect , semigroup , mathematical analysis , pure mathematics , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , gene , medicine , linguistics , philosophy , nonlinear system

This paper studies the asymptotic stability of a repairable system withrepair 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 eigenvalue0

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