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

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.