How perturbations in the matrix of linear systems of ordinary differential equations propagate along solutions

This paper addresses how perturbations in the matrix A propagate along the solution of the n-dimensional linear ordinary differential equation y′(t)=Ay(t),t≥0,y(0)=y0.In other words, for fixed t≥0 and y0∈Rn, we study the conditioning of the problem A↦etAy0.We also study the asymptotic behavior of the conditioning as t→+∞. The analysis is carried out for a normal matrix A.