Journal of Systems Science and Complexity

, Volume 20, Issue 3, pp 437–443 | Cite as

Exponential Stability of a Reparable Multi-State Device

  • Weiwei HuEmail author
  • Houbao Xu
  • Jingyuan Yu
  • Guangtian Zhu


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.


C0-semigroup exponential stability irreducibility quasi-compact 


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Copyright information

© Springer Science + Business Media, LLC 2007

Authors and Affiliations

  • Weiwei Hu
    • 1
    Email author
  • Houbao Xu
    • 2
  • Jingyuan Yu
    • 1
  • Guangtian Zhu
    • 3
  1. 1.Beijing Institute of Information and ControlBeijingChina
  2. 2.Department of MathematicsBeijing Institute of TechnologyBeijingChina
  3. 3.Academy of Mathematics and Systems Science, Chinese Academy of SciencesBeijingChina

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