Robust Output Feedback Control Design in the Presence of Sporadic Measurements

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. A linear matrix inequalities-based design methodology for the codesign of the gains of the controller and the parameters of the holding device is presented. The effectiveness of the proposed design approach is showcased in a numerical example.