  The main purpose of this paper is to obtain necessary and sufficient
conditions under which a nonautonomous, finite-dimensional and two-sided
dynamics generated by a sequence of matrices or a linear ODE exhibits
Hyers-Ulam stability. Specifically, in the case of discrete time we consider a
nonautonomous difference equation with possibly noninvertible coefficients,
while in the case of continuous time we deal with a nonautonomous ordinary
differential equation without any bounded growth assumptions.
