Optimal tracking with finite control energy for sampled-data systems

In this paper, the optimal tracking problems with finite control energy for sampled-data system which is non-minimum-phase and unstable are studied. Some new analytical results are derived for the step signals. It is shown that the optimal performance is related with the non-minimum phase zeros and unstable poles of the continuous plant. In addition, the nonminimum phase zeros from sampling and hold operations and the unstable poles from discretizaion also occupy an important position. The weight factor between the tracking error energy and the control energy plays an important role in the explicit expression of the optimal performance. At last, one example is given to validate the conclusions.