Stabilization of networked control systems over a sharing link using ALOHA

In this paper we consider a networked control model which has multiple plant-controller pairs, each pair´s plant and controller being separated. All the sampled data transmissions share a common single link. Instead of deterministic/centralized scheduling, all the plant-controller pairs use the link in a random access fashion (particularly, according to a simplified version of ALOHA), as in generic data networks. The sampled data packets suffer from possible collisions in the random link access, thus the resulting sampling processes have random interarrival times. We argue that the stabilization problem can be solved in a two-stage manner. First, for each single plant-controller pair, a necessary and sufficient condition is derived for its (mean-square) stability under random sampling. Second, for multiple pairs altogether, it is shown that the existence of simultaneous stabilizing policies corresponds to the feasible solution set of a series of inequality constraints.