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

• Published in: IEEE transactions on automatic control pp. 1 - 8
• Main Authors: Guaracy, Fernando H. D., Ferreira, Luis H. C.
• Format: Journal Article
• Language: English
• Published: IEEE 2025
• Subjects: Actuators; Asymptotic stability; Mean-square stability; Networked control system; Networked control systems; Numerical stability; Nyquist plot; Packet loss; Robustness; Sensitivity; Stability analysis; Stochastic processes; Stochastic systems; Thermal stability
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2025.3590803

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 <inline-formula><tex-math notation="LaTeX">\mathcal {H}_{\infty }</tex-math></inline-formula> norm of sensitivity and complementary sensitivity functions. We also analyze guaranteed mean-square <inline-formula><tex-math notation="LaTeX">S</tex-math></inline-formula>-based and <inline-formula><tex-math notation="LaTeX">T</tex-math></inline-formula>-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.