Topological Conditions for In-Network Stabilization of Dynamical Systems

摘要: We study the problem of stabilizing a linear system over wireless network using simple in-network computation method. Specifically, we an architecture called "Wireless Control Network" (WCN), where each node maintains state, and periodically updates it as combination neighboring plant outputs states. This has previously been shown to have low computational overhead beneficial scheduling compositionality properties. In this paper characterize fundamental topological conditions allow stabilization such scheme. To achieve this, exploit fact that WCN scheme causes act dynamical system, analyze coupling between plant's dynamics network. show control inputs can be computed if vertex connectivity is larger than geometric multiplicity any unstable eigenvalue plant. condition analogous typical min-cut required in classical information dissemination problems. Furthermore, specify equivalent for wired (or point-to-point) employs coding traditional way - communication mechanism sensors decentralized controllers at actuators.