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

• Published in: IEEE control systems letters Vol. 7; pp. 1646 - 1651
• Main Authors: Seuret, Alexandre, Tarbouriech, Sophie
• Format: Journal Article
• Language: English
• Published: IEEE 2023
• Subjects: Closed loop systems; Data collection; Data driven control; Linear matrix inequalities; Linear systems; Mathematics; Robust control; saturated systems; Stability criteria; Symmetric matrices; Uncertainty; Data driven control, Robust control, saturated systems
• ISSN: 2475-1456
• DOI: 10.1109/LCSYS.2023.3267022

This letter revisits the <inline-formula> <tex-math notation="LaTeX">\mathcal {L}_{2} </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">\mathcal {L}_{2} </tex-math></inline-formula>-gain stabilization of the closed-loop system is addressed by considering a static state-feedback control law. Then, the <inline-formula> <tex-math notation="LaTeX">\mathcal {L}_{2} </tex-math></inline-formula>-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.