Linear output regulation of discrete-time networked systems subject to stochastic packet drops

We investigate a scenario in which a given discretetime controller communicates with a discrete-time plant via a wireless erasure channel in a linear scenario. The controller is designed for the output of the plant to track a periodic reference generated by a finite superimposition of discretetime linear oscillators while rejecting additional disturbances, i.e., to solve an output regulation problem. Due to stochastic packet drop induced by the network, the closed-loop behavior switches between two different dynamical systems, depending on the probability of transmission. We show that, when packet drops occur on the channel from the controller to the actuator, the exogenous signal implies that the expected regulation error does not go to zero but converges to a ball centered at zero. Differently, when the packet drops are on the output channel, we provide a set of sufficient conditions such that the regulation error asymptotically shrinks to zero in expectation. Results are validated via numerical examples.