A poset framework to model decentralized control problems

In a previous paper, these authors showed that posets provide a useful modeling framework for a reasonably large class of decentralized control problems. In this paper we show more connections between posets and decentralized control. Firstly, we show that previously known results about systems with time delays follow naturally using the poset framework. We also mention extensions of this to infinite-dimensional spatio-temporal systems. Secondly, we study conditions under which the properly known as quadratic invariance and poset structure are equivalent. Through this paper, we hope to convince the reader of the important role that posets seem to play in much of the current theory of decentralized control.