Classical Control System Analysis Over Lossy Networks: An Easy-to-Use Nyquist Plot Approach

• Published in: IEEE transactions on automatic control Vol. 68; no. 6; pp. 3783 - 3789
• Main Authors: Ferreira, Luis H. C., Guaracy, Fernando H. D.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-06-2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Asymptotic stability; Control systems; Data transmission; Linear matrix inequalities; Mathematical analysis; Mean-square stability; Network control; networked control system; Norms; Numerical stability; Nyquist plot; Nyquist plots; Packet loss; Sensitivity; Stability analysis; Stability criteria; Stochastic systems; Systems analysis; Transfer matrices; Upper bounds
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2022.3195679

This article presents an approach based on the Nyquist plot to analyze the mean-square stability of a networked control system in which data transmission is subject to the occurrence of packet losses. This result is obtained by translating well-known linear matrix inequality (LMI) conditions for mean-square stability to conditions that take the form of upper bounds on the <inline-formula><tex-math notation="LaTeX">\mathcal {H}_{\infty }</tex-math></inline-formula> norms of the sensitivity and complementary sensitivity transfer matrices. Although the results obtained provide only sufficient conditions, the proposed approach allows us to inspect if the stochastic feedback system is mean-square stable by conveniently using classical Nyquist plots. A numerical example is given to illustrate the ease of use of the proposed tool.