Tracking with an H^∞ criterion

We study the problem of tracking a reference signal from the H∞ point of view. As opposed to general H^∞ problems, where only suboptimal solutions are obtained, we show that, for both the full information and measurement feedback tracking problems the H^∞-optimal solutions can be explicitly found. The results also indicate an interesting dichotomy between minimum phase and non-minimum phase plants: for minimum phase plants the best causal tracker performs as well as the best noncausal tracker, whereas for non-minimum phase plants, causal trackers cannot reduce the H^∞ norms from their a priori values. We also mention some remedies for the non-minimum phase case, such as adding more actuators (control inputs) or allowing for some finite delay. For causal tracking of non-minimum phase plants, we show that a delay equal to at least the number of non-minimum phase zeros of the plant is required