Trade-off performance analysis of LTI system with channel energy constraint

In this paper, the trade-off performance between tracking error, control input energy and channel input power is studied. By modelling the communication channel as the additive coloured Gaussian noise channel (ACGN) with limited bandwidth, a new performance index is proposed and minimized over all stabilizing two-degree-of-freedom controllers. The results show that the trade-off performance is correlated to the intrinsic characteristics of the plant, including the locations and directions of the unstable pole, non-minimum phase zero. However it is unrelated to the non-minimum phase zeros of filter because of the two-degree-of-freedom controller. We also demonstrated that ACGN may degenerate the tracking performance. Finally, a typical example is given to validate the theoretical results. •A new performance index is proposed and minimized over all stabilizing controllers.•It shows that tradeoff performance depends on non-minimum phase zero and unstable pole.•The tradeoff performance is unrelated to the non-minimum phase zeros of filter.•The white noise dramatically worsens systems׳ tracking performance.•The results are helpful for the design of controllers and communication channel.