I can't understand this simplification the book says without explanation. Could someone help me?
It is the calculatation/development of the transfer function of a digital system composed by a dac (digital-to-analog converter, using a zero-order hold), analog subsystem [G(s)] and an adc (analog-to-digital converter, using a sampler).
L^{-1} is the operator of inverse laplace transform, Z in the operator o Z transform and the '*' means the function in sampled (discrete time).
I just wrote the last two lines.
The book is 'Digital Control Engineering' from Sam Fadali.