Stabilization of distributed networked control systems with minimal communications network

In this paper we study general stability condition of distributed networked control systems with minimum number of necessary communication links. We use the Lyapunov direct method to find a general stability condition that guarantees the asymptotic stability of the entire networked control system and then use binary programming to design a communications network with minimum number of links that satisfies the general stability condition. Reducing the number of communication links implies minimization of the communications network's cost and energy consumption . The results apply to networks of linear time-invariant (LTI) systems.