Consensus tracking for singular multi‐agent systems with Lipschitz nonlinear dynamics and external disturbances

• Published in: International journal of robust and nonlinear control Vol. 32; no. 8; pp. 4899 - 4922
• Main Authors: Liu, Tianya, Sheng, Andong, Ma, Cui‐Qin, Qi, Guoqing, Li, Yinya
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 25.05.2022
• Subjects: consensus tracking; directed network; Disturbances; Dynamical systems; extended state observer; Linear matrix inequalities; Lipschitz nonlinearity; Mathematical analysis; Nonlinear dynamics; Nonlinearity; singular multi‐agent systems; Stability analysis; State observers; System theory; Systems theory; Tracking control
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.6060

The consensus tracking control problem for singular multi‐agent systems (SMASs) with Lipschitz nonlinearities and unknown disturbances is investigated. An extended state observer using only the relative output information is introduced and then a distributed consensus protocol is proposed, whose performance is analyzed using matrix analysis, singular system theory and Lyapunov stability theory. Sufficient conditions for ensuring consensus tracking with disturbance rejection of linear and Lipschitz nonlinear SMASs are, respectively, obtained under directed networks. Specifically, an equivalent formulation of achieving consensus tracking for SMASs is established, and the design procedures of gain matrices in the proposed consensus protocols are presented by the linear matrix inequality solver. Finally, simulation examples are provided to illustrate the theoretical results.