Tracking with an H 1 Criterion 1

In this paper we study the problem of tracking a reference signal from the H 1 point of view. As opposed to general H 1 problems, where only suboptimal solutions are obtained, we show that for both the full information and measurement feedback tracking problems the H 1-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 1 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 nite 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.