Real-time reachable set estimation for linear time-delay systems based on zonotopes

This paper considers reachable set estimation for discrete-time linear time-delay systems. With the assumption that the unknown initial condition and disturbances are bounded by zonotopes, three zonotope-based methods are proposed to estimate the real-time reachable sets. We find that the couplings in the time-delay systems lead to conservative estimation results and propose a reachable set estimation method based on state augmentation. The augmentation-based method can reduce the conservatisms caused by the time-delay and achieve more accurate reachable set estimation. Simulation results demonstrate the performances of the proposed methods.