Semi-convergence matrix error bound

Question

I have matrix A_nxn with the following properties:

1. primitive (the corresponding graph is strongly connected and has at least 2 coprime length cycles).
2. non-negative
3. largest eigenvalue equal to 1, and it's simple, and strictly greater than others in absolute value.
4. Not symmetric, and the corresponding graph is not regular

I have the following equation: X(t+1) = A*X(t) (X is vector). Also we can write: X(t) = A^(t)*X(0) This equation semi-convergence when t->infinity (convergence to the eigenvector V1 corresponding to the eigenvalue 1).

My question is: There is any analytic upper bound of the error: E = norm(A^(t)*X(0) - V1) ? Especially with graph structure interpretation.