First of all, it's a rare topic in google, so I can't find intuitive explanation about step-invariant, so I don't understand actually what it is, except to solve zero order hold transfer function.
In this pdf, page 15 to 18 I've been learning about zero order hold (ZOH). http://www.engr.usask.ca/classes/EE/480/notes/myee480-p4-sampleHold.pdf
As you can see above, suddenly the laplace transform has become starred, why does it happened?
First thought, I think it was like distributive starred property. But why suddenly it has a star while you still have starred curly bracket? Is it a typo?
And also, from the wikipedia
It's written that $X^*(s) = L[x(t).dirac_T(t)] = L[x^*(t)]$
The star is only on the big X and small x, and it's not on the L one, so why the creator made it star on the L one?
Furthermore, if you also take a look at page 17 (top right). First, (1-e^-Ts) are converted into laplace transformation form, and then it gets starred, and then it is separated, and then it return to the first original (1-e^-Ts) form. What's the use? It's seems illogical.
If you don't mine, please also explain intuitively what is step-invariant z-transform and why the creator use step-invariant z-transform method to find the transfer function and not the other method.