  The matrix differential equation $x'(t) = Q(t)x(t), x(0) = x_0$ is considered
in the case where $Q(t)$ is an unspecified matrix function of time, with the
only constraint that $Q(t)\in \mset$ for every $t$, where $\mset$ is a
prescribed closed and convex set of matrices. We provide the solution of the
generalised equation by defining an exponential of a set of matrices. Although
the defintion is not directly applicable to calculate the solutions, we provide
an approximate method along with the estimation of maximal possible error. In
particular, the method allows estimating continuous time imprecise Markov
chains.
