Continuous selections of trajectories of hybrid systems

摘要

We present results on existence of continuous selections of trajectories of hybrid systems evolving according to Lipschitz nonlinear inclusions. First, we utilize the Skorohod metric to define both a family of pseudo-metrics and a metric on the set of trajectories accepted by the hybrid automaton. We show that under a non-Zeno condition the latter metric is complete. Second, the existence of continuous selections with respect to the family of pseudo-metrics is proved under a relatively mild assumption of transversality. (C) 2002 Elsevier Science B.V. All rights reserved. [References: 10]