Abstract:

A fourunit redundant system with commoncause was discussed. First we transformed the system to an abstract Cauchy problem in a Banach space. Second, by analyzing the spectrum of the system operator and its dual operator, the authors proved that 0 was unique spectral point on the imaginary axis and the others spectra lie on the left side of the complex plane. As a result, the asymptotic stability of the fourunit redundant system with commoncause was obtained.

Key words: dual space, adjoint operator, eigenvalue, geometric multiplicity