Distributed robust control of linear multi-agent systems with parameter uncertainties

• Main Authors: Li, Zhongkui, Duan, Zhisheng, Xie, Lihua, Liu, Xiangdong
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2013
• Subjects: DRNTU::Engineering::Electrical and electronic engineering
• Online Access: https://hdl.handle.net/10356/96737; http://hdl.handle.net/10220/11590
• Institution: Nanyang Technological University

This article 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 neighbouring 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 ∞ 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 ∞ control problems of uncertain linear multi-agent systems subject to external disturbances are discussed.