Suppose I have a real (physical) dynamical system with some sensors and actuators, and I also have an idealized state-space model of this same system. How, in general, can I adjust the model to match the real system?

My experience is with frequency-domain analysis. My first reaction would be to measure swept-sine transfer functions, and to calculate parameters of my system from the location of resonances or poles in the measured data.

Is there a better, more general technique for system identification in the state-space representation?

  • $\begingroup$ Is the system assumed to be linear? If it is, then a frequency response should be sufficient to characterize it. $\endgroup$
    – Jason R
    Apr 13, 2012 at 15:08
  • $\begingroup$ Yes, but how do you put the experimental frequency domain data into the state space form? $\endgroup$
    – nibot
    Apr 13, 2012 at 15:34

1 Answer 1


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.


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