Solution:

$\boxed{\frac{39}{2}}$

Note that when a piece of paper is folded in half, one pair of opposite sides is preserved and the other pair is halved. Hence, the net effect on the perimeter is to decrease it by one of the side lengths. The original perimeter is $2\left(\frac{17}{2}\right) + 2 \cdot 11 = 39$. By considering the cases of folding twice along one edge or folding once along each edge, one can see that this perimeter can be decreased by at most $11 + \frac{17}{2} = \frac{39}{2}$. Hence, the minimal perimeter is $\frac{39}{2}$.