Optimal guaranteed cost control for interconnected large-scale systems under networked gossip protocol

In this note, the optimal guaranteed cost control problems for interconnected systems subject to gossip scheduling protocol are studied. For each subsystem, gossip protocol can decide the communication order of various neighbors. Each subsystem’s local controller at every instant will select only one neighboring sub-controller to transfer its subsystem’s state information. Some sufficient conditions are performed so as the closed-loop interconnected system achieves exponential stability and the cost function is less than a certain maximal value. All the distributed controller gains are designed according to the solutions of the developed linear matrix inequality conditions. Finally, the developed theoretical results are verified via the given example.