Leader-Following Consensus of Nonlinear Multi-Agent Systems Based on Parameterized Lyapunov Function

Tabari Saadi, Pegah; Mardani, Mohammad Mehdi; Shasadeghi, Mokhtar; Safarinejadian, Behrouz

Leader-Following Consensus of Nonlinear Multi-Agent Systems Based on Parameterized Lyapunov Function

Authors

P. Tabari Saadi

M. M. Mardani

M. Shasadeghi

B. Safarinejadian

Department of Electrical and Electronics Engineering, Shiraz University of Technology, Shiraz, Iran

Abstract

This paper studies the consensus problem of nonlinear leader-following multi-agent systems (MAS). To do this, the error dynamics between the leader agent and follower ones are described via a Takagi-Sugeno (TS) fuzzy model. If the obtained TS fuzzy model is stable, then all of the nonlinear agents reach consensus. The consensus problem is investigated based on the parameterized or fuzzy Lyapunov function combined with a technique of introducing slack matrices. The slack matrices cause to decouple the Lyapunov matrices from systems ones and therefore, sufficient consensus conditions are obtained in terms of linear matrix inequalities (LMIs). The proposed slack matrices add an extra degree-of-freedom to the LMI conditions and also decrease the conservativeness of the LMI-based conditions. Finally, in order to illustrate the effectiveness and merits of the proposed method, a numerical example for the consensus problem of nonlinear leader-follower MAS with thirteen followers is solved.

Keywords

Nonlinear multi-agent systems

Consensus

Takagi-Sugeno (T-S) fuzzy model

Parameterized Lyapunov function

Linear Matrix Inequality (LMI)