Stabilizability over deterministic relay networks

We consider the problem of linear system stabilization using a set of decentralized controllers that communicate with the plant's sensors over a network that employs linear network coding. Our analysis is built upon an existing algebraic description of deterministic relay networks, which is able to model broadcast transmissions and multiple access channel constraints. Since these networks can be described as linear time-invariant systems with specific transfer functions, this network representation allows us to reason about the control system and network (and their interaction) using a common mathematical framework. In this paper we characterize algebraic and topological stabilizability conditions for a wide class of these networks. Our analysis shows that the (algebraic) structure of a network required for stabilization of a dynamical plant can be related to the plant's dynamics; in particular, we prove that the geometric multiplicities of the plant's unstable eigenvalues play a key role in the ability to stabilize the system over such networks.