On the asymptotic behavior of linear systems
Phil Locke · Proceedings of the American Mathematical Society · 1970
The purpose of this paper is to establish a necessary and sufficient condition for the vector-matrix system x ˙ = [ A ( t ) + B ( t ) ] x \dot x = [A(t) + B(t)]x to have solutions of the form Y ( t ) c ( t ) Y(t)c(t) where Y ( t ) Y(t) is a fundamental matrix of solutions of y ˙ = A ( t ) y \dot y = A(t)y .