LQG cheap control over SNR-limited lossy channels with delay

In this paper we study the effect of communication nonidealities on the control of unstable stochastic scalar linear systems. The communication protocol links the sensors to the actuators and should be studied by taking into account several limitations such as quantization errors, limited channel capacity, decoding/computational delays and packet loss. We restrict our analysis in the context of LQG cheap control subject to SNR limitations, packet loss, and delay and we derive their impact on optimal design for the controller parameters. In particular, we show that the stability of the closed loop system depends on a tradeoff among quantization, packet loss probability and delay. Through this analysis we are also able to recover, as special cases, several results already available in the literature that have treated packet loss, quantization error and delay separately.