Unified form of performance limitations in reference tracking control problem for discrete time systems

This paper deals with tracking performance of linear time-invariant discrete time SISO systems. In the existing results, the fundamental limitations are analyzed based on the knowledge of reference signals such as the step, the trigonometrical signals and so on. Our purpose is to find the closed form expressions of the tracking performance limitation for the general class of reference inputs. Moreover, the closed form expressions clearly separate the contributions of the plant and the reference characteristics. In discrete time setting, we can derive not only the optimal tracking performance but also the optimal controller. Effectiveness of the results are shown by examples.