There are some problems here, possibly caused by a terminological confusion, I'm not sure exactly what:
With a unit delay in your feedback path (implicit), a filter is more prone to instability with the pole/zero coefficients.
Implicit methods yield distortion in the higher frequencies (as you approach nyquist), which can be attenuated with oversampling, but which can be more or less avoided with a ZDF.
(Maybe similar to the previous...) A ZDF gives you better accuracy with the cutoff frequency and resonance (for 2+ order filters), especially near Nyquist.
A ZDF yields a smoother time-varying filter response than an implicit filter method with a unit-delay.
The words "implicit/explicit" in that literature are used in the sense mentioned here https://en.wikipedia.org/wiki/Explicit_ ... it_methods
and "ZDF" basically means finding a solution to an implicit equation. It may further be used in a sense to refer to certain other design criteria imposed upon the solution( https://www.native-instruments.com/file ... pology.pdf
) , implicitly. (It's even further implicit in that in practice it often refers to simulation of a moog synth filter without explicitly mentioning it each time.) These are some of the different senses it may be "implicit" about.
A further distinction can be made between analytical and numerical/iterative solutions as mentioned here https://math.stackexchange.com/question ... o-problems
A "closed form" solution refers to the same concept as "analytical solution" (https://en.wikipedia.org/wiki/Closed-form_expression
Basically that's the terminology and there may even be further names that refer to the same concepts. Application of each method yields a solution with different properties.
That literature obviously has much more content than simply noting these, but without noticing the proper interpretation of the terminology it sounds more mystical than it actually is.
Returning to the paper(s) that has possibly confused you, read these sentences from the above paper again:
A trivial approach is commonly in use here, to simply put additional z−1 delays into the offending feedback paths. This often results in acceptable transfer functions, except for the high frequency areas and/or certain values of system parameters, where the transfer function gets distorted beyond reasonable, often leading to unstable systems.
As you can see these sentences refer to an explicit solution, not "a traditional implicit one".