Jing Chena, Hongfen Zoub 'An interesting method for the exponentials for some special matrices'

Systems Science & Control Engineering., 2014, Vol. 2, 2–6.Abstract
The matrix exponential eAt plays a central role in linear system and control theory. This paper develops a method to compute the accurate solution for the matrix exponential eAt with the assumption that the matrix A has an eigenvalue s1 exactly zero. The examples show the effectiveness of the proposed method.