M16.6 Summary

The unit circle plays the same role in discrete-time systems that the real line does in continuous-time systems. A zero outside the unit circle causes the same performance limitations that an RHP zero causes for continuous systems. It is possible, however, for a continuous-time system with no RHP zero to have a discrete zero that is outside the unit circle, if the continuous-time system has a relative order of 3 or higher.

Discrete-time models with zeros outside the unit circle must be factored into the bad stuff for discrete IMC controller design. This procedure is similar to continuous-time models, where RHP zeros must be factored into the bad stuff. The main difference between continuous and discrete systems is that even zeros than are inside the unit circle, but negative, must be factored out; if they are not, the controller will often be too oscillatory for acceptable performance.