Structured-LMI conditions for stabilizing network-decentralized control

In this paper we consider a set of dynamically decoupled systems interconnected by control agents. We can visualize this architecture as a graph where subsystems are associated to nodes and control agents are associated to arcs. The interconnection between subsystems is determined by their input matrix. The decisions of each control agent can directly affect only the nodes connected by the corresponding arc. We seek a stabilizing control framework in which each control agent has information only about the state components associated with the nodes it influences; we say this control architecture is decentralized in the sense of networks. This problem setup involves block-structured feedback matrices, with structural zero blocks. We provide a constructive, sufficient condition based on an LMI with block-diagonal constraints, which guarantees stabilizability through a network-decentralized state-feedback control law. We show that under some structural conditions, concerning local stabilizability and connection with the external environment, the LMI condition we provide is always feasible. Thus, the desired controller can be found in an efficient way.