CAJ | 학술논문

应用泛函分析的方法讨论了有两个相同部件和一个热储备的并行可修复系统的指数稳定性.我们通过分析系统算子生成C0半群的本质谱增长阶,证明了该半群是拟紧的.此外,该半群还是不可约的.于是作为半群拟紧性和不可约性的直接结果,得到了系统的时间依赖解指数收敛到其静态解,并且该静态解即为系统算子简单特征值0对应的正的特征向量.
응용범함분석적방법토론료유량개상동부건화일개열저비적병행가수복계통적지수은정성.아문통과분석계통산자생성C0반군적본질보증장계,증명료해반군시의긴적.차외,해반군환시불가약적.우시작위반군의긴성화불가약성적직접결과,득도료계통적시간의뢰해지수수렴도기정태해,병차해정태해즉위계통산자간단특정치0대응적정적특정향량.
A repairable system associated with two identical units parallel and one warm standby is studied from the viewpoint of linear semigroup theory in this paper. We present that the C0-semigroup generated by the system operator is quasi-compact by analyzing its essential growth bound. Further, it is also irreducible. The steady-state solution is known to be the positive eigenfuction corresponding to the simple eigenvalue 0 of the system operator. As a result, the exponential stability of the system is obtained.