Data-Driven Control of Discrete-Time Systems With Time-Varying Delay Under Multiple Data Perturbations

This article investigates the problem of data-driven control design for unknown linear discrete-time systems with time-varying delays, where the controller gains are learned from input-state data affected by multiple perturbations. First, considering that the available measurements may be affected by noise, errors, and timing mismatches, a data-based parametric representation is constructed to characterize the set of all systems consistent with the collected perturbed data that contains the true system. Then, using the obtained data-based representation, the delay-dependent data-driven control design problem is addressed by applying the Lyapunov-Krasovskii functional method and linear matrix inequality technique, ensuring closed-loop stability for all systems in the admissible set. Finally, a case study on a batch reactor is provided to demonstrate the effectiveness and advantages of the proposed control approach.