Input saturated control of time-delay systems: a data-driven approach

This paper introduces a data-driven static output-feedback (SOF) control framework for continuous-time linear time-delay systems subject to input saturation. The proposed controller design is carried out by input-state-output data-based delay-dependent Linear Matrix Inequality (LMI) conditions derived using the Lyapunov-Krasovskii stability theory and the generalised sector condition. The key distinctive feature of the proposed methodology is its ability to achieve direct control synthesis without requiring prior knowledge of the system dynamics. This is accomplished by avoiding variable transformations, equality constraints, or iterative algorithms, thanks to a novel data-based representation of continuous-time delay systems and the strategic application of Finsler's Lemma. Furthermore, the method improves safety guarantees by providing an estimate of the admissible initial condition region, ensuring local asymptotic stability of the origin despite input saturation.The effectiveness of the proposed control strategy is illustrated through its application to a generic linear time-delay system and the stabilisation of an underactuated VTOL aircraft, highlighting its potential for real-world applications.