Classical Control System Analysis Over Lossy Networks: Guarantees of Stability and Robustness Margins

This article presents an analysis of mean-square stability and robustness margins for networked systems. We consider an architecture in which the controller-to-actuator channel is subject to packet losses, and a zero-input strategy is used to deal with the losses. For this situation, we obtain guaranteed mean-square gain and phase margins based on the $\mathcal {H}_{\infty }$ norm of sensitivity and complementary sensitivity functions. We also analyze guaranteed mean-square $S$-based and $T$-based disk margins, which in the case of single-input, single-output systems and losses modelled by Bernoulli processes can be translated into a tool based on Nyquist plots. A numerical example is presented to illustrate the use of the proposed results.