Robust Output Feedback Control Design in the Presence of Sporadic Measurements

• Published in: IEEE transactions on automatic control 2023-06, Vol.68 (6), p.1-8
• Main Authors: Merco, Roberto, Ferrante, Francesco, Sanfelice, Ricardo G., Pisu, Pierluigi
• Format: Article
• Language: English
• Subjects: Automatic Control Engineering; Availability; Closed loop systems; Closed loops; Co-design; Computer Science; Control systems; Feedback control; Feeds; Holding devices; Hybrid systems; Linear matrix inequalities; Numerical stability; Output feedback; Perturbation; Robust control; Stability analysis; Symmetric matrices; Time invariant systems; Time measurement
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2022.3213616

Output feedback control design for linear time-invariant systems in the presence of sporadic measurements and exogenous perturbations is addressed. To cope with the sporadic availability of measurements of the output, a hybrid dynamic output feedback controller equipped with a holding device whose state is reset when a new measurement is available is designed. The closed-loop system, resulting from the interconnection of the controller and the plant, is augmented with a timer variable triggering the arrival of new measurements and its properties are analyzed using hybrid system tools. Building upon Lyapunov theory for hybrid systems, sufficient conditions for internal and \mathcal {L}_{2} input-to-output stability are proposed. An LMI-based design methodology for the co-design of the gains of the controller and the parameters of the holding device is presented. The effectiveness of the proposed LMI-based design approach is showcased in a numerical example.