Some results on minimum magnitude regulated response

Analytical results are obtained for the minimum peak tracking error magnitude achievable by some finite settling time control systems in response to a step reference input. The limits of these results as the settling time approaches infinity are also obtained. These represent performance bounds which apply for any finite order linear time-invariant (LTI) controller of a given configuration (i.e., one-parameter or two-parameter). The systems considered are one-parameter discrete-time single-input, single-output (SISO) where the plant has one unstable pole and one non-minimum-phase zero. The result for a two-parameter compensator for plants with one non-minimum-phase zero is presented