Low Complexity Invariant Sets for Time-Delay Systems: A Set Factorization Approach

This chapter deals with the study of invariant sets for discrete time linear systems affected by delay. It establishes a new perspective on their structural properties via set factorization. This novel perspective describes, in a unified framework, different existing notions of invariant sets. Additionally, it is shown that the (possible non-minimal) state space representation is a key element in the description of low complexity invariant sets.