Synchronization of Perturbed Linear Systems with Data-Rate Constraints

In this paper, we consider the synchronization of two linear systems that are subject to unknown perturbations. One of the systems is driven by a reference signal, which is unknown to the second system. Both systems can only use a one-way communication channel to exchange information. The channel is subject to data-rate constraints. The messages are generated by a smart sensor that measures the state and is capable of performing some computations. The messages are received by a controller which interprets them to apply an appropriate control input to the system. The objective is to design a sensor/controller pair, which we will refer to as a communication protocol, such that the distance between the states of both systems is bounded, and as small as possible communication rate is necessary. In this paper, a communication protocol that achieves this objective is presented together with the minimum channel rate to implement it. Simulations of the communication protocol are provided to support the theoretical work.