Exponential Stability of a Reparable Multi-State Device

Hu, Weiwei; Xu, Houbao; Yu, Jingyuan; Zhu, Guangtian

doi:10.1007/s11424-007-9039-9

Cited by 28 publications

(9 citation statements)

References 3 publications

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“…And then, we may know that many repairs/services are done periodically in practice. So we can suppose that the mean of repair/service rate exists and does not equal to 0 ( [15,16]):…”

Section: Mathematical Model Formulationmentioning

confidence: 99%

The Well-Posedness and Stability Analysis of a Computer Series System

Qiao

Zheng

et al. 2013

Journal of Applied Mathematics

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A repairable computer system model which consists of hardware and software in series is established in this paper. This study is devoted to discussing the unique existence of the solution and the stability of the studied system. In view ofc0semigroup theory, we prove the existence of a unique nonnegative solution of the system. Then by analyzing the spectra distribution of the system operator, we deduce that the transient solution of the system strongly converges to the nonnegative steady-state solution which is the eigenvector corresponding to eigenvalue 0 of the system operator. Finally, some reliability indices of the system are provided at the end of the paper with a new method.

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“…And then, we may know that many repairs/services are done periodically in practice. So we can suppose that the mean of repair/service rate exists and does not equal to 0 ( [15,16]):…”

Section: Mathematical Model Formulationmentioning

confidence: 99%

The Well-Posedness and Stability Analysis of a Computer Series System

Qiao

Zheng

et al. 2013

Journal of Applied Mathematics

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“…With the method in [9] it can be easily proved that the domain D(A) of A + E is dense in X. It remains to prove that A + E is a dispersive operator.…”

Section: Description Of the Systemmentioning

confidence: 99%

Exponential stability of a repairable system with N failure modes and K standby units

Zhao

Guo

Qiao

et al. 2012

2012 24th Chinese Control and Decision Conference (CCDC)

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This paper is devoted to studying the existence, uniqueness and exponential stability of repairable system's time-dependent solution. By analysis the spectrum of the system operator generated by the repairable system, we derive that zero is the unique spectral point on the imaginary axis and the other spectral lie on the left half plane. The positive contraction strongly continuous semigroup which is generated by the operator corresponding to these equation is a quasicompact operator. As a result, we get the desired result that the dynamic solution of the system exponentially tends to the steady solution.

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“…The dual space of X is as follows: 21 ; O n;nþ1 Þ; D 21 ¼ ðl 1 ðyÞ; l 2 ðyÞ; Á Á Á ; l n ðyÞÞ T ; D 3 ¼ diagðbðzÞ; bðzÞ; Á Á Á ; bðzÞÞ 1;n;…”

Section: Asymptotic Stability Of the Systemmentioning

confidence: 99%

Stability analysis of a new kind n-unit series repairable system

Guo

Gao

et al. 2011

Applied Mathematical Modelling

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a b s t r a c tIn this paper, we deal with a new model of an n-unit series repairable system, in which a concept of a repairman with multiple-delayed vacation is introduced and the impact on the system reliability due to a replaceable facility is also considered. This paper is devoted to studying the unique existence and stability of the system solution. C 0 -semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by analyzing the spectra distribution of the system operator, we prove that the dynamic solution of the system asymptotically converges to the nonnegative steady-state solution which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Furthermore, we discuss the exponential stability of the system in a special case. Some reliability indices of the system are also studied and the optimal vacation time is analyzed at the end of the paper.

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Exponential Stability of a Reparable Multi-State Device

Cited by 28 publications

References 3 publications

The Well-Posedness and Stability Analysis of a Computer Series System

The Well-Posedness and Stability Analysis of a Computer Series System

Exponential stability of a repairable system with N failure modes and K standby units

Stability analysis of a new kind n-unit series repairable system

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