Switched mRPI Sets are Strictly Contained in Time-Delay mRPI Sets

摘要

Ahstract- We examine the relationship between the minimal robust positively invariant sets, mRPI, of discrete-time switched and time-delay systems. Assuming the existence of the mRPI sets for each system, we show that the mRPI set of a finitely many sub-system switched system is strictly contained in the mRPI of a corresponding time delay system. We further demonstrate that the minimal convex robust positively invariant set of either a time-delay or, the corresponding, switched system is the convex hull of the mRPI of either system.