Exponential Stability of Single-Module Repairable System with Warning State

被引：0
|
作者：
Liu D.-X. [1 ,2 ]
Wang L.-H. [1 ]
Jia Y. [1 ]
Zhang J.-W. [1 ]
机构：
[1] State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang
[2] College of Science, Yanbian University, Yanji
来源：
Dongbei Daxue Xuebao/Journal of Northeastern University | 2018年 / 39卷 / 07期
关键词：
C[!sub]0[!/sub] semigroup; Compact operator; Essential spectrum bound; Exponential stability; Perturbation;
D O I：
10.12068/j.issn.1005-3026.2018.07.009
中图分类号：
学科分类号：
摘要：
A kind of single-module repairable system with warning state was investigated, which can be expressed as a set of differential equations. By selecting the appropriate state space and the definition domain of the system operator, the equations were transformed into an abstract Cauchy problem in a Banach space. With the functional analysis method and linear operator semigroup theory, the eigenvalue 0 was proved to be the strictly dominant simple eigenvalue of the system. It shows the solution of the system is asymptotically stable. Then by studying the spectrum distribution of the main operator of the system, it was proved that the essential spectrum bound of the main operator of the system is negative. Finally, the variation of essential spectrum bound of the main operator under compact perturbation were discussed. The results demonstrate that the dynamic solution of the system is exponentially stable. © 2018, Editorial Department of Journal of Northeastern University. All right reserved.
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页码：954 / 958
页数：4
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