On the reachable set bounding of uncertain dynamic systems with time-varying delays and disturbances

In this paper, improved conditions are proposed for finding an ellipsoidal bound of reachable sets which bound the state trajectories of uncertain dynamic systems with time-varying delays and bounded peak disturbances. A more generalized time-derivative condition is considered in comparison with previous work. By the use of convex-hull properties and application of the Lyapunov method, sufficient conditions for finding an ellipsoidal bound of reachable sets of the concerned systems are established in terms of linear matrix inequalities (LMIs). Two numerical examples are included to show the superiority and effectiveness of our results.