Spectral characterizations for Hyers-Ulam stability

First we prove that an n x n complex linear system is Hyers-Ulam stable if and only if it is dichotomic (i.e. its associated matrix has no eigenvalues on the imaginary axis iR). Also we show that the scalar differential equation of order n, x((n))(t) - a(1)x((n-1))(t) + ... + a(n-1)x'(t) + a(n)x(t), t is an element of R+ :- [0,infinity), is Hyers-Ulam stable if and only if the algebraic equation z(n) = a(1)z(n-1) + ... + a(n-1)z + a(n) has no roots on the imaginary axis.