The Asymptotical Stability Of a Warm Standby System with Priority in Use And Repair
作者单位：Population Theory Staff in Center for Population and Family Planning Cadre Training The Logisitics College Department of Mathematics Tianjin University
会议名称：《第25届中国控制与决策会议》
主办单位：IEEE;NE Univ;IEEE Ind Elect Chapter;IEEE Harbin Sect Control Syst Soc Chapter;Guizhou Univ;IEEE Control Syst Soc;Syst Engn Soc China;Chinese Assoc Artificial Intelligence;Chinese Assoc Automat;Tech Comm Control Theory;Chinese Assoc Aeronaut;Automat Control Soc;Chinese Assoc Syst Simulat;Simulat Methods & Modeling Soc;Intelligent Control & Management Soc
会议日期：2013年
学科分类：0839[工学-网络空间安全] 08[工学] 081201[工学-计算机系统结构] 0812[工学-计算机科学与技术（可授工学、理学学位）]
基 金：supported by the National Science Natural Foundation in China(NSFC-61174080)
关 键 词：Linear operator C0 Semigroup Well-Posedness Asymptotic Stability
摘 要：In this paper we consider a warm standby repairable system that consists of two dissimilar components and one repairman. Suppose that the life of each component satisfies the exponentially distribution and the repair time of the component satisfies the general distribution, the component 1 has priority in use and repair. Firstly, a mathematical model is built via the differential and partial differential equations, then by using the C0 -semigroup theory and analyzing the spectra distribution of the system operator, the unique existence of the solution is derived. Then the non-negative steady-state solution and the asymptotic stability of the system are derived.