A Data-Driven Approach to the L₂ Stabilization of Linear Systems Subject to Input Saturations

Abstract

This paper revisits the L2 stabilization problem for linear systems subject to saturating input and energy-bounded additive disturbance from a data-driven point of view. The backbone of the results resides in writing the stability conditions in a compact dedicated structure allowing to exhibit LMI conditions. Based on the assumption that the data collection is informative, the finite L2-gain stabilization of the closed-loop system is addressed by considering a static state-feedback control law. Then, the L2-gain of the closed loop and an inner-approximation of the basin of attraction of the origin for the disturbance-free closed-loop system are characterized. The potential of the method is discussed along the treatment of an academic example.