Stabilization of a collection of linear systems with communication constraints

A new approach is introduced in this paper for the stabilization problem of a collection of linear systems which operate under limited communication. Each linear system is viewed as a user on an idealized shared network which grants access only to a few users at a time. To solve the problem, there are two lines of research undergone: one is to give a sufficient condition for the existence of stabilizing control sequences and show how they can be constructed in a way that minimizes network usage; the other is to determine the capacity of the network in order to serve the collection of systems under consideration. The novelty of the iterative approach lies in that the controllers are designed to make full use of the old information to stabilize the entire collection when the network channel is not available for some of the system members to transmit their state measurements. The method we propose is easy to be applied in real practice.