Finite-time positiveness and distributed control of Lipschitz nonlinear multi-agent systems

• Published in: Journal of the Franklin Institute Vol. 356; no. 15; pp. 8080 - 8092
• Main Authors: Ren, Chengcheng, Nie, Rong, He, Shuping
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.10.2019; Elsevier Science Ltd
• Subjects: Control systems design; Controllers; Finite element analysis; H-infinity control; Liapunov functions; Linear matrix inequalities; Mathematical analysis; Matrix; Matrix methods; Multiagent systems; Nonlinear control; Nonlinear systems; Performance indices
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2019.06.044

The finite-time positiveness and distributed control problem is studied for a class of Lipschitz nonlinear multi-agent systems. The objective is to design a suitable distributed controller which makes the closed-loop multi-agent systems be positive and finite-time stabilizable and satisfy the given H∞ performance index. Sufficient conditions are initially established on the existence of the finite-time distributed controller by using proper multiple Lyapunov functions and the design criteria are presented in the form of linear matrix inequalities. Finally, an example of multi-agent systems with six agents is presented to illustrate the feasibility and validity of the proposed methods.