Exponential Stability of A Multi-state System with Two Repair Distributions
The well-possedness and exponential stability of the solution to a multi-state system with two repair distributions were discussed by applying the Co semigroups theory of function analysis. First, the integro-differential equations described the system was transformed into some abstract Cauchy problem on some suitable Banach space. Second, by Hill-Yosida Theorem, the system operator generates a positive contractive Co semigroups and the result of wellpossedness of the system was obtained. Last, the spectral distribution of the system operator was analyzed. It was proven that 0 is strictly dominant eigenvalue of the system operator and the result of the dynamic solution of the system exponentially converges to the steady one was got since the spectral growth bound is less than zero.
repairable system Co semigroups well-possedness exponential stability
Fu Zheng
Department of Mathematics Bohai University Jinzhou,Liaoning Province,China Institute of Information and Control Beijing,China
国际会议
南京
英文
393-396
2010-08-26（万方平台首次上网日期，不代表论文的发表时间）