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Robustness analysis and distributed control of a networked system with time-varying delays

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Abstract

This paper is concerned with the robustness analysis and distributed output feedback control of a networked system with uncertain time-varying communication delays. This system consists of a collection of linear time-invariant subsystems that are spatially interconnected via an arbitrary directed network. Using a dissipation inequality that incorporates dynamic hard IQCs (integral quadratic constraints) for the delay uncertainties, we derive some sufficient robustness conditions in the form of coupled linear matrix inequalities, in which the coupled parts reflect the interconnection structure of the system. We then provide a procedure to construct a distributed controller to ensure the robust stability of the closed-loop system and to achieve a prescribed 2-gain performance. The effectiveness of the proposed approach is demonstrated by some numerical examples.

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Correspondence to Tong Zhou.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 61573209, 61733008).

Zhike WANG received the B.Sc. degree in Electrical Engineering and Automation and the M.Sc. degree in Navigation, Guidance and Control from Air Force Engineering University, Xi’an, China, in 2005 and 2009, respectively. He is currently working toward the Ph.D. degree at the Department of Automation, Tsinghua University, Beijing, China. His main research interest includes the fields of robust stability analysis and distributed control of networked systems.

Tong ZHOU received the B.Sc. degree in Automatic Control and the M.Sc. degree in Control Theory and Applications from the University of Electronic Science and Technology of China, Chengdu, China, in 1984 and 1989, respectively, and the M.Sc. degree in Electrical and Computer Engineering from Kanazawa University, Kanazawa, Japan, in 1991, and the Ph.D. degree in Industrial Machinery from Osaka University, Osaka, Japan, in 1994. After visiting several universities in the Netherlands, China, and Japan, he, in 1999, joined Tsinghua University, Beijing, China, where he is currently a Professor of control theory and control engineering. His current research interests include robust estimation and control, system identification, signal processing, hybrid systems, and their applications to real-world problems in molecular cellbiology, spatiotemporal systems, magnetic levitation systems, and communication systems. Dr. Zhou was a recipient of the First-Class Natural Science Prize in 2003 from the Ministry of Education, China, and a recipient of the National Outstanding Youth Foundation of China in 2006. He was an Associate Editor for the IEEE Transactions on Automatic Control, and is currently on the Editorial Board of Automatica.

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Wang, Z., Zhou, T. Robustness analysis and distributed control of a networked system with time-varying delays. Control Theory Technol. 18, 293–306 (2020). https://doi.org/10.1007/s11768-020-9109-2

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  • DOI: https://doi.org/10.1007/s11768-020-9109-2

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