State space system identification
The experimental frequency domain data gives you information on the input-output behavior of the system. If the system is assumed to be linear and time-invariant (LTI), this information will be in the form of a transfer function. Given a transfer function, there are infinitely many state-space realizations that yield the same input-output behavior and, thus, are I/O-equivalent.

Having said that, you may want to take a look at the Adaptive Control literature.