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

Abstract

In this paper,the reliability of a periodically repairable robot system with safty device is disscussed.Using the method of functional analysis,especially the linear operator theory and C_0 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.