In this paper we consider the problem of controlling multiple scalar systems through a limited capacity shared channel. Each system is affected by process noise and can be controlled byactuators with values in a {\em fixed}inite set. The control objective is to bound the evolution of the systems in specified sets (controlled invariance). Our goal is to find an optimal allocation of the shared communication resource to the different control activities and to identify correct choices for the design parameters. The paper provides fundamental conceptual tools to attack the design problem in the formal framework of an optimization problem. Namely, we give a feasibility criterion to decide whether a set of design parameters conforms with a control specification (i.e., with the controlled invariance of a specified set for each system). Moreover, we offer the explicit computation of the minimum bit rate necessary for the controlled invariance of a set, which is of utmost importance for solving the optimization problem.

%B Proc. IEEE Int. Conf. on Decision and Control %P 1448-1453 %G eng