Exponential Stability of k Out of N: G Redundant System

Abstract

In this paper we investigate the dominant eigenvalue and stability of $k$ out of $N: G$ redundant system with repair facilities and multiple critical and non-critical errors. By using the method of functional analysis, especially, the linear operator theory on Banach space, we prove the existence of strictly dominant eigenvalue of the system. We show that the dynamic system is linear stable and exponential stable.