On the design of control systems over unreliable channels

This paper studies LTI one-degree-of-freedom networked control architectures built around LTI SISO plants. The feedback path comprises an unreliable channel that drops data in an i.i.d. fashion. We extend known results to show that there exists a second order moments equivalence between the situation examined and an auxiliary feedback loop where the unreliable channel has been replaced by an additive i.i.d. noise channel that has an equality signal-to-noise ratio constraint. We then use these insights to design optimal controllers. We also establish a necessary and sufficient condition on the successful transmission probability that allows for the design of a controller that guarantees MSS in the considered setup. Our proposal does not require packet arrival acknowledgements. Thus, our results give necessary and sufficient conditions for MSS in an output-feedback control architecture with UDP-like protocols.