Exponential stability of a reparable multi-state device

Weiwei Hu; Houbao Xu; Jingyuan Yu; Guangtian Zhu

doi:10.1007/s11424-007-9039-9

Exponential stability of a reparable multi-state device

Weiwei Hu^*, Houbao Xu, Jingyuan Yu, Guangtian Zhu

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

40 Citations (Scopus)

Abstract

The exponential stability of a multi-state device is discussed in this paper. We present that the C ₀-semigroup generated by the system operator is quasi-compact and irreducible. It is known that 0 is a simple eigenvalue of the system operator. In combination with this, we obtain that the time-dependent solution exponentially converges to the steady-state solution, which is the positive eigenfuction corresponding to the simple eigenvalue 0.

Original language	English
Pages (from-to)	437-443
Number of pages	7
Journal	Journal of Systems Science and Complexity
Volume	20
Issue number	3
DOIs	https://doi.org/10.1007/s11424-007-9039-9
Publication status	Published - Sept 2007

Keywords

C -semigroup
Exponential stability
Irreducibility
Quasi-compact

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10.1007/s11424-007-9039-9

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Hu, W., Xu, H., Yu, J., & Zhu, G. (2007). Exponential stability of a reparable multi-state device. Journal of Systems Science and Complexity, 20(3), 437-443. https://doi.org/10.1007/s11424-007-9039-9

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N2 - The exponential stability of a multi-state device is discussed in this paper. We present that the C 0-semigroup generated by the system operator is quasi-compact and irreducible. It is known that 0 is a simple eigenvalue of the system operator. In combination with this, we obtain that the time-dependent solution exponentially converges to the steady-state solution, which is the positive eigenfuction corresponding to the simple eigenvalue 0.

AB - The exponential stability of a multi-state device is discussed in this paper. We present that the C 0-semigroup generated by the system operator is quasi-compact and irreducible. It is known that 0 is a simple eigenvalue of the system operator. In combination with this, we obtain that the time-dependent solution exponentially converges to the steady-state solution, which is the positive eigenfuction corresponding to the simple eigenvalue 0.

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KW - Exponential stability

KW - Irreducibility

KW - Quasi-compact

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Exponential stability of a reparable multi-state device

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Keywords

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