In a paper of me of a few years ago, <i>[Estimate on the Pathwise Lyapunov Exponent of Linear Stochastic Differential Equations with Constant Coefficients][1]</i>, Theorem 3.6 gives sufficient conditions. The proof is indeed by iteration, but of the continuous time Lyapunov equation, which I found gave better results in the case I was interested in.

These sufficient conditions are, in terms of your notation:
$\sum_{i=1}^p ||F_i||^2 < 1$, which looks very similar to the condition you state but is perhaps more restrictive. Unfortunately at the moment I am not too fluent in Kronecker products, so I find it difficult to compare.


  [1]: http://www.tandfonline.com/doi/abs/10.1080/07362994.2010.503453#.U-CrTNYvDRY