Robustness analysis and distributed control of a networked system with time-varying delays
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Control Theory and Technology http://link.springer.com/journal/11768
Robustness analysis and distributed control of a networked system with time-varying delays Zhike WANG 1,2 , Tong ZHOU 1† 1.Department of Automation, Tsinghua University, Beijing 100084, China; 2.School of Aviation Operations and Services, University of Air Force Aviation, Changchun Jilin 130022, China Received 18 June 2019; revised 16 January 2020; accepted 22 May 2020
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. Keywords: Networked system, time delay, integral quadratic constraints (IQCs), robust stability, distributed control DOI https://doi.org/10.1007/s11768-020-9109-2
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Introduction
Recently, the rapid developments in computer networking technology and control engineering have enabled many large-scale networked systems (LSNS), such as unmanned flight formations, automated highway systems, satellite constellations, and smart structures. The common features of these systems are that they usually consist of numerous subsystems and exhibit complex dynamic behavior as a whole by exchanging information
among the subsystems through the interconnection networks. When controlling these systems, it is often necessary to adopt a distributed architecture, in which the controller is also composed of several interconnected units, to take advantage of structure information and reduce the computation or communication complexity. Great effort has been devoted to investigating the stability analysis and distributed controller synthesis problems for special types of systems, including spatially
† Corresponding author. E-mail: [email protected]. This work was supported by the National Natural Science Foundation of China (Nos. 61573209, 61733008).
© 2020 South China University of Technology, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature
Z. Wang, T. Zhou / Control Theory Tech, Vol.
invariant systems [1–4], strongly interconnected systems [5], identical dynamically coupled or decoupled systems [6, 7], heterogeneous spatially distributed systems [8, 9]. Most distributed control approaches assume that the communication is ideal. However, due to the spat
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