SOME RESULTS ON MINIMUM MAGNITUDE REGULATED RESPONSE

In this note, analytical results are obtained for the minimum peak tra cking error magnitude achievable by some finite settling time control systems in response to a step reference input. The limits of these res ults as the settling time approaches infinity are also obtained. These are of interest since they represent performance bounds which apply f or any finite order LTI controller of a given configuration (i.e., one -parameter or two-parameter). These limiting results have been previou sly given only as the numerical solution to be obtained from an infini te linear program. The systems considered are one-parameter discrete-t ime SISO where the plant has one unstable pole and one nonminimum phas e zero. The result for a two-parameter compensator for plants with one nonminimum phase zero is also presented.