Discrete inversion formulas for the design of lead and lag discrete compensators

In the paper, new discrete inversion formulas suitable for the design of lead and lag discrete compensators in the frequency domain are presented. These formulas can be very useful for teaching in Automatic Control courses. The links of these discrete formulas with the continuous inversion formulas are deeply investigated. A simple graphical procedure for the design of discrete compensators on the Nyquist plane is also presented. Finally, some numerical examples illustrate the presented results.