Set theory based condition in LMI form for network topology preservation for decentralized control

Connectivity preservation of the interconnection network is an essential ingredient in decentralized control. This paper focuses on the preservation of a given network topology which ensures the connectivity. We consider a networked system with a discrete dynamics in which two subsystems are able to communicate if an algebraic relation between their states is satisfied. The connected subsystems are called neighbours. The subsystems updates their state in a decentralized manner by taking into account their neighbours state. Each connection is preserved as far as the algebraic relation is verified. The objective of the proposed set theory based control law is to keep the state of each subsystem in a specific domain that ensures the algebraic constraint satisfaction. The resulting control design reduces to the solution of convex problems involving Linear Matrix Inequalities (LMI), then easily solvable. Beside the network preservation, the global coordination may be imposed by adding supplementary constraints in the control design.