Further Tracking Results for Input-constrained Minimum-Phase Systems

Minimum phase systems are the only systems that allow (in disturbance-free unconstrained case) the achievement of perfect tracking in presence of arbitrary reference signals. The question is whether this still holds when the control input is subject to input saturation constraint. Surprisingly, most works on global output tracking in presence of input saturation focused on nonminimum phase systems. Then, perfect tracking is only achievable for constant references. In this paper, it is shown that more powerful tracking results are achievable for minimum phase systems. Specifically, perfect tracking is guaranteed for arbitrary type reference signals that satisfy a well defined strict compatibility condition. When, the reference signal is just compatible in the mean then the tracking quality depends on the reference variation rate. For periodic reference signals (not necessarily compatible with constraint), all the closed-loop system signals are shown to be periodic with the same period.