Robust consensus for linear multi-agent systems with structured uncertainties

• Published in: International journal of control Vol. 94; no. 3; pp. 675 - 686
• Main Authors: Xue, Xiangming, Wu, Fen, Yuan, Chengzhi
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 04.03.2021; Taylor & Francis Ltd
• Subjects: Algorithms; bilinear matrix inequality; distributed control; Iterative methods; Linear matrix inequalities; Linear systems; Mass-spring-damper systems; Mathematical analysis; Multiagent systems; Optimization; Output feedback; output-feedback protocol; Robust control; structured uncertainty; Synthesis; Uncertain linear multi-agent systems; Uncertainty
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207179.2019.1612096

This paper addresses a robust consensus problem for linear multi-agent systems subject to structured uncertainty and external disturbances under the leaderless framework. A distributed dynamic output-feedback protocol is proposed, which utilises not only relative output information of neighbouring agents but also relative state information of neighbouring controllers. Through model transformations, the robust consensus control problem of multi-agents network is reduced to a set of independent stabilisation problems for single linear subsystems. For robust consensus, it is shown that the analysis and full state-feedback synthesis conditions for such subsystems can be formulated as linear matrix inequality (LMI) optimisation problems. On the other hand, the synthesis condition for dynamic output-feedback protocol is formulated as non-convex bilinear matrix inequality (BMI) optimisation problem. An iterative LMI algorithm is then presented to solve the resulting BMI optimisation problem. An example of multiple mass-spring-damper systems has been used to demonstrate theoretical results.