SMPS input impedance as function of frequency
So my question is what are the parameters and phenomenons affecting
  the input impedance of a SMPS as a function of frequency and how to
  mathematically deal with them?


This has made me think a little (a dangerous thing!). An SMPS of the type in the TI document is basically a DC-to-DC converter and not an AC-to-DC converter. I wanted to make that clear so there is no misunderstanding of what I'm talking about in my answer.

By input impedance, we have to "consider" applying a small sinewave on top of the DC input voltage and then analysing things. That small sinewave will be "modulated" by the switching action inside the converter and you'll get a signal (before the LC output filter of the switcher) that looks something like this: -



Clearly this is only the AC part of the output waveform; it will of course be superimposed on a DC voltage. Now, if you perfectly low pass filtered the AC waveform you would obtain a sinewave of exactly the same frequency as the inputted sinewave but smaller in amplitude. 

The reduction in amplitude is because of the switching converter's duty cycle but, this is of no consequence because the real point is that a switching converter will still output a frequency that corresponds with the sinewave superimposed on the input voltage.

OK so far?

So, what happens when this "modified" sinewave meets the LC filter on the output of the converter. I call it an LC filter because that is exactly what it is: -



Yes, the L and the C form a fundamental part in transferring energy from the switched waveform to the steadier DC output but it's still an LC filter.

That LC low pass filter will be fairly high Q. In other words, it is capable of being very resonant because the DC losses in the inductor are, by design, intentionally small and additionally, it is well understood that the LC natural resonant frequency MUST be significantly lower than the lowest switching frequency. If the switching frequency were largely coincident with the resonant frequency then you have a major problem because the LC will act as a series resonant network directly from switching node to 0V and this will devastate functionality.

So, if the small sinewave transferred (by switching action) to the input of the LC has a frequency coincident with the natural resonant frequency of that LC then you theoretically have a switcher with zero input impedance.

This is why an SMPS of the type in the document (e.g. any buck regulator) will naturally have an input impedance that drops to quite a low value at some particular frequency and, this frequency is determined fundamentally by the output filter resonant frequency.

Added to this is the input decoupling capacitor across the input wires of any switching converter. In other words there is a general falling of input impedance as frequency rises. Given also that the switching transistor won't have zero ohms on resistance there is a slight lessening of the resonant effect described above.