A discrete system (transfer function) with poles of negative real part presents non-sinusoidal oscillations

PID controllers are optimal but not robust at all

The theoretical discretization method is the most complicated one

The interpolation method in the D/A converter determines the plant discretization

Diverse continuous systems can replicate the operation of a discrete system

All the discretization methods map the continuous into the discrete poles according to the theoretical definition

The interpolation method in the A/D converter determines the plant discretization method

Dead-beat controllers are very robust but non-optimal

The theoretical discretization method is the simplest one

All the infinite continuous left semiplane (s variable) is compressed into the discrete unit circle (z variable)