I am starting to read about Floquet theory and its basic setup
$\dot{x} = A(t) x$
where $A(t)$ is a $N$-dimensional $T$-periodic bounded square matrix for all $t$ and $x \in \mathbb{R}^N$.
I was wondering why I do not (yet) see the solution
$x(t) = e^{\int_0^t A(s) ds} x(0)$
written anywhere. Here, I use the matrix exponential. Is there something wrong with this construction?