摘要
研究了一类具有优化调整状态的供应链系统的指数稳定性.通过选取空间和定义算子,将模型方程转变成了抽象Cauchy问题.首先运用预解正算子理论,证得该系统主算子和系统算子均为预解正算子,再利用共尾定理证明主算子的谱界与增长界相等.然后运用相关代数知识证得0为系统算子的简单本征值.同时通过研究系统算子的谱特征,证明了系统算子的谱点均位于复平面的左半平面且虚轴上除0外无谱,进而得到系统的渐进稳定性.最后,由半群展开定理得到系统的指数稳定性.
The paper presents a supply chain system with state of optimal adjustment. By choosing space and defi- ning operator of this system, we transfer this model into an abstract Cauchy problem. Using resolvent positive opera- tor theory, we first prove both the main operator and the cording to cofinal theory we show that the spectral bound system operator are resolvent positive operators. Then ac- of the main operator is the same as its growth bound. Fur- thermore, we prove that 0 is the simple eigenvalue of the system operator. By spectral analysis of the system, we find that 0 is the unique spectral point of system on the imaginary axis. As a result, the asymptotic stability of such maintenance system is proved. Finally, we obtain the exponential stability of the system using expansion theorem of semigroup.
作者
冯志瑞
原文志
FENG Zhi-rui YUAN Wen-zhi(Department of Mathematics, Taiyuan Normal University, Jinzhong 030619, China)
出处
《烟台大学学报(自然科学与工程版)》
CAS
2017年第4期273-281,共9页
Journal of Yantai University(Natural Science and Engineering Edition)
关键词
供应链
预解正算子
共尾
谱分布
指数稳定性
supply chain
resolvent positive operator
cofinal
spectral distribution
exponential stability