具有周期修复的机器人系统指数稳定性分析

Analysis of Exponential Stability to the Robot System with Periodic Repair Function

研究具有周期修复函数的机器人与其连带的安全装置构成的系统的可靠性.运用泛函分析的方法,特别是Banach空间上的线性算子半群C_0理论,证明了系统的适定性,并通过分析系统本质谱和经过扰动后半群的本质谱半径的变化,给出解的有限展开式。并进一步证明,0是系统的严格占优本征值,系统的非零本征值至多有两个,从而表明系统解以指数形式收敛.

In this paper, the reliability of a periodically repairable robot system with salty device is disscussed. Using the method of functional analysis, especially the linear operator theory and C0 semigroup theory on the Banach space, the well-posedness of solution to the system is proved, the finite espansion of the solution is obtained by the analysis of the essential spectrum to the system and the change of essential spectrum radius of semigroup under perturbation, furthermore we prove that 0 is the strictly dominant eigenvalue of the system and there are two nonzero eigenvalues of the system at most. therefore we show the sulution to the system converge exponentially.