Exponential Stability Of A Robot With Safety System

This paper presents a system that containing a robot and its associated safety mechanism. The system have various modes of failures and is repairable. There is no standby unit in the system. Through modifying operator, it has more practical significance. By using strongly continuous semi-group theory and Sobolev space theory, The paper investigate the nonnegative stead-state solution of system, the existence of strictly dominant eigenvalue and restriction of essential spectrum growth bound of the system operator. The essential spectral radius of the system operator is also discussed before and after perturbation. The result show that the dynamic solution of the system is exponential stability and converges to the stead-state solution.