Improved Reachable Set Bounding for Linear Systems with Discrete and Distributed Delays

This paper addresses the problem of reachable set bounding for linear systems in the presence of both discrete and distributed delays. The time delay is assumed to be differentiable and vary within an interval. By using the Lyapunov-Krasovskii approach and delay decomposition technique, improved delay-dependent conditions for the existence of an ellipsoid-based bound of reachable sets of the system trajectories are derived in terms of matrix inequalities. Here, the new idea is to minimize the ellipsoids’ projection distances on each axis with different exponential convergence rates, instead of minimizing the ellipsoidal radius with a single exponential rate. A smaller bound can thus be obtained from the intersection of these ellipsoids. The effectiveness of the proposed approach is illustrated by a numerical example.