Improved reachable set bounding for linear time-delay systems with disturbances

In this paper, we reconsider the problem of reachable set bounding for linear time-delay systems with disturbances. Generalized reachable sets for dynamical systems are proposed where initial points are taken into account. Meanwhile, a novel lemma is given which shows an extended criterion that the reachable sets are bounded. Then, based on this lemma and the Lyapunov-Krasovskii functional (LKF) as well as the free-weighting matrix techniques, improved delay-dependent linear matrix inequality (LMI) criteria are obtained for finding an ellipsoid to bound the reachable sets of linear time-delay systems with disturbances. Two numerical examples are finally provided to substantiate the efficiency and merits of our theoretical results.