FIR estimator for IIR system Suppose that we have a dynamical system of which the impulse responses are infinite (IIR). Now I found methods on papers (http://dx.doi.org/10.1109/9.839942) estimating states or outputs of such a system with a FIR estimator. So this FIR estimator gives me approximately the same (state) output as my original system. 

I find it hard to conceive how an estimator with only poles in $z_i=0$ is able to duplicate a system with poles $|z_i|&lt;1$ (but not necessarily $z_i=0$). I think it has something to do with interpolation conditions, but I would really appreciate it if someone could make this clear to me. Thanks :)

I understand that for a stable dynamical system IIR will decay to zero and thus can be truncated to FIR. But my question remains how a FIR could 'mimic' the poles of an IIR?
Simply truncating the impulse response of an IIR filter will give the optimal $\ell_2$ FIR approximation to the IIR system.

Whether this form of approximation is good enough to "mimic" the IIR system depends on what you mean by that.