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

摘要

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. (C) 2016 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.