可修复人机系统的指数稳定性

发布时间：2018-05-21 05:17

  本文选题：预解正算子 + 谱分布　； 参考：《数学的实践与认识》2017年02期

【摘要】：研究了两相同部件温储备可修的人机系统,运用C_0半群的相关理论,对系统主算子的谱界进行估值.估算系统的算子产生的半群的增长界,然后运用了共尾的概念及相关的理论,得到了系统算子A+B的谱界与系统算子产生的半群的增长界相同.进而运用相关代数知识证得,0为系统算子的简单本征值,并分析了系统算子的谱分布,得到系统的指数稳定性.并研究了系统算子预解式的特性.对任意给定的δ0,γ=a+bi,-μ+δa_1≤a≤a_2,得到lim|b|→∞‖R(γ;A+B)‖=0.进而得到在~sRγ≥a_1的右半平面内相应于系统算子A+B的谱点由有限个本征值组成.
[Abstract]:In this paper, the repairable man-machine system with two same components is studied, and the spectral bound of the main operator of the system is estimated by using the theory of C _ s _ 0 semigroup. The growth bounds of Semigroups generated by system operators are estimated. Then by using the concept of cotail and related theories, the spectral bounds of system operators A B and the growth bounds of Semigroups generated by system operators are obtained. Then we prove that 0 is the simple eigenvalue of the system operator by using the knowledge of correlation algebra. The spectral distribution of the system operator is analyzed and the exponential stability of the system is obtained. The properties of the resolvent of the system operator are studied. For any given 未 _ 0, 纬 -a bibior- 渭 未 _ a _ s _ 1 鈮，

本文编号：1917893