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arXiv · 1109.3781

Distributed Robust Control of Linear Multi-Agent Systems with Parameter Uncertainties

Zhongkui Li·Zhisheng Duan·Lihua Xie·Xiangdong Liu
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Abstract

This paper considers the distributed robust control problems of uncertain linear multi-agent systems with undirected communication topologies. It is assumed that the agents have identical nominal dynamics while subject to different norm-bounded parameter uncertainties, leading to weakly heterogeneous multi-agent systems. Distributed controllers are designed for both continuous- and discrete-time multi-agent systems, based on the relative states of neighboring agents and a subset of absolute states of the agents. It is shown for both the continuous- and discrete-time cases that the distributed robust control problems under such controllers in the sense of quadratic stability are equivalent to the $H_\infty$ control problems of a set of decoupled linear systems having the same dimensions as a single agent. A two-step algorithm is presented to construct the distributed controller for the continuous-time case, which does not involve any conservatism and meanwhile decouples the feedback gain design from the communication topology. Furthermore, a sufficient existence condition in terms of linear matrix inequalities is derived for the distributed discrete-time controller. Finally, the distributed robust $H_\infty$ control problems of uncertain linear multi-agent systems subject to external disturbances are discussed.

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Zhongkui Li, Zhisheng Duan, Lihua Xie, Xiangdong Liu. 2011-09-17. Distributed Robust Control of Linear Multi-Agent Systems with Parameter Uncertainties. https://arxiv.org/abs/1109.3781

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