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- W1967961335 abstract "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<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$C_0$ id=E1><mml:msub><mml:mi>C</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math>-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<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$0$ id=E2><mml:mn>0</mml:mn></mml:math>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<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$0$ id=E3><mml:mn>0</mml:mn></mml:math>." @default.
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- W1967961335 date "2005-01-01" @default.
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- W1967961335 title "Asymptotic stability of a repairable system with imperfect switching mechanism" @default.
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- W1967961335 doi "https://doi.org/10.1155/ijmms.2005.631" @default.
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