When I was reading through the RECOM book of knowledge DC-DC, I found
out that the SEPIC converter has more chance of having resonance
feedback than the ZETA converter. Why has the ZETA a more stable
The ZETA has a more stable output (less ripple, or as they say, "resonance feedback") because the inductor is directly in line with the output, and as we know, an inductor resists changes in current, and therefore smooths it out.
The SEPIC has a more stable INPUT (less ripple, or as they say, "resonance feedback") because the inductor is directly in line with the input, and therefore smooths it out.
For powering LED's with battery power, the SEPIC is actually better because high ripple on the input wastes the battery, and many LED's do just fine with high ripple as long as their specifications are not exceeded, and our eyes average out the response as long as the frequency is high enough.
It just depends on where you want your ripple to be -- on the input or the output.
And you can choose the CUK to get low ripple at both ends, or add your own filter to improve the other end as needed.