| 冷贮备可修复系统解的指数渐近稳定性 |
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| 引用本文： | 胡晓晓,谢观湧.冷贮备可修复系统解的指数渐近稳定性[J].浙江师范大学学报(自然科学版),2012(3):258-263. |
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| 作者姓名： | 胡晓晓 谢观湧 |
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| 作者单位： | 温州医学院信息与工程学院 |
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| 摘 要： | 讨论了具有两同型部件的冷贮备可修复系统，首先证明系统算子可以生成正压缩C0半群T（t）；接着证明了T（t）是拟紧算子，且0是对应系统的主算子及其共轭算子的几何重数与代数重数为1的特征值．由此推出：该系统的时间依赖解，当时间趋向于无穷时，以指数形式收敛于系统的稳态解．
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| 关 键 词： | 冷贮备可修复系统 C0半群 拟紧算子 共轭算子 |
Exponential asymptotic stability of the solution of a cold standby repairable system |
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| HU Xiaoxiao,XIE Guan.Exponential asymptotic stability of the solution of a cold standby repairable system[J].Journal of Zhejiang Normal University Natural Sciences,2012(3):258-263. |
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| Authors: | HU Xiaoxiao XIE Guan |
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| Institution: | yong(School of Information and Engineering,Whenzhou Medical College,Whenzhou Zhejiang 325035,China) |
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| Abstract: | It was discussed a cold standby repairable system with two identical components.The system were described by a group of partial equations with integral boundary conditions.Firstly,it was showed that the operator corresponding to the system generated a positive contraction C0-semigroup T(t),and proved that T(t) was a quasi-compact operator.Secondly,it was verified that 0 was an eigenvalue of this operator and its adjoint operator with geometric and algebraic multiplicity one.Lastly,by using the above results,the time-dependent solution of the system strongly converged to the steady-state solution was established. |
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| Keywords: | cold standby repairable system C0-semigroup quasi-compact adjoint operator |
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