Network coding meets decentralized control: Capacity-stabilizabililty equivalence

The main difference between centralized and decentralized control is the communication. Controllers in a decentralized system can communicate with each other to achieve their common goal. In this paper, we argue that even linear time-invariant controllers in a decentralized linear system “communicate” via linear network coding to stabilize the plant. To justify this argument, we propose an algorithm to “externalize” the implicit communication between controllers that we believe must be occurring to stabilize the plant. Based on this, we show that the stabilizability condition for decentralized linear systems comes from an underlying communication limit, which can be described by an algebraic mincut-maxflow theorem.