Data-dependent reachable set estimation for linear time-delay systems with unknown system matrices

This paper investigates data-driven reachable set estimation (RSE) for linear time-delay systems with unknown system matrices and bounded disturbances. Offline input–state data are used to design a state-feedback controller and construct an ellipsoidal outer bound without identifying the system matrices. A two-stage method is proposed. In the first stage, the feedback gain and Lyapunov matrix are obtained from data while accounting for unknown disturbances in the offline dataset. In the second stage, linear matrix inequality conditions determine the reachable-set bound under state delay and bounded online disturbances. The framework is further extended to event-triggered control, where an ellipsoidal reachable-set bound and a positive lower bound on the inter-event time are derived to exclude Zeno behaviour. Numerical examples, including a satellite system, demonstrate the effectiveness of the proposed method.