Scheduling for Stabilization over Capacity-Constrained Channels

We address the problem of stabilizing a set of discrete-time systems over a communication network. The network consists of capacity-constrained discrete-time Additive White Gaussian Noise (AWGN) channels. We consider the case when the number of channels is limited and propose a dynamic scheduling scheme that, at a given time, determines which subset of systems get access to the channel for feedback control. This problem is addressed by considering two separate problems - scheduling systems over noiseless channels and stabilizing a system over an AWGN channel. The scheduling problem is addressed in the switched system framework by making use of a min-type Lyapunov function. We provide a sufficient condition in the form of Linear Matrix Inequalities (LMIs) to schedule a subset of systems while achieving stability of all systems. We also explicitly determine the scheduling scheme. Next, we provide a novel LMI-based necessary and sufficient condition for stabilization of a discrete-time system over a discrete-time AWGN channel. Finally, we appropriately combine the two results to obtain an LMI-based sufficient condition for the join scheduling-stabilization problem.