Dear Rannam,
I can’t think of a good reference that explains “aerodynamic stiffness.”
It is a bit peculiar to me that the stiffness matrix is not symmetric. This may be a result of the way the quasi-steady induction is recalculated with every perturbation in the linaerization process (and may not be realistic). In some cases, it is more accurate to assume a frozen wake during linearization–see, for example, the forum topic found here: Gain Scheduling. I suggest you see if your linearization results are drastically different with frozen wake. If so, I would use the results with frozen wake.
Best regards,