Stabilization by controller networks

This paper addresses a problem of finding a controller network to stabilize linear time-invariant plants. Here, the controller network means an architecture that networked controllers cooperatively determine the control input applied to a plant by exchanging the information with their neighbors. As a solution to this problem, we propose a controller network which acts as a state feedback controller by a dynamic consensus algorithm. By combining a coordinate transformation including a parameter and Gershgorin theorem, we derive a condition for the gain to stabilize the resulting feedback system. We also present a relation between the stabilizing gain and the network topology. These results will be useful for designing a controller network that is robust against changes in the network topology. Finally, the validity of these results is demonstrated by numerical simulations.