When passing from analogous transfer function to digital transfer functions several methods are currently used, e.g. bilinear transform, impulse response-invariance method, and Euler method (EM). The last consists in replacing the complex variable s by

$({z}^{-1}-1)/{\Delta}=\delta $, where z is the shift operator,

${\Delta}$ is the sampling interval and

$\delta $ is the so-called

$\delta $ operator. It is well known that EM gives satisfactory results when the poles are located near the point

$1+j\xb70$ in the z-plane, what is equivalent to use a sampling rate equal to near 10 times the filter bandwidth. In the paper it is shown that EM has some advantages over the other methods when simulating control systems. Some numerical examples clearly show these advantages (superior roundoff noise performance, less sensitive control design). Also, it is shown that the

$\delta $ operator method allows a better understanding of the link between the continuous and discrete-time approach to system analysis.