SISO Linear System Control via Saturating Actuator: L2 Tracking Performance in Presence of Arbitrary Shape Inputs

International audienceMost studies on linear system control in the presence of actuator saturation have focused on closed-loop asymptotic stabilisation. Available tracking results are generally limited to constraint-compatible inputs (references, disturbances) with known exogenous input models. The problem of output-reference tracking in the presence of arbitrary-shaped not necessarily constraint-compatible inputs has yet to be investigated. In this study, we show that an tracking performance is achievable for SISO linear systems using a given class of saturated controllers. Accordingly, the tracking error energy (resp. power) is bounded by the energy (resp. power) of a well-defined mismatch input depending on the disturbance and reference compatibility. In the disturbance-free case, this entails perfect asymptotic tracking of arbitrary-shaped constraint-compatible reference signals. Otherwise, the average tracking quality is proportional to the mismatch input power. In the case of periodic inputs (constraint-compatible or not), all system signals are shown to be periodic with the same period as the inputs