On Robustness of Pre-Asymptotic Stability to Delayed Jumps in Hybrid Systems

We show that pre-asymptotic stability of a compact set for a hybrid system is semiglobally and practically robust in the presence of delayed jumps under mild conditions on the data. More precisely, when the delay-free system has a pre-asymptotically stable compact set, it is shown that for small enough delays, solutions of the delayed system converge to a neighborhood of a set of interest related to the aforementioned compact set. Unlike prior work, this notion of practical stability also holds for time-varying delays in the presence of Zeno solutions. Simulation results of a state estimator with intermittent and delayed information validate the findings.