A fuzzy approach on consensus of nonlinear leader-follower multi-agent systems

A linear matrix inequality based approach for consensus of leader follower nonlinear multi-agent systems is discussed in this paper. A nonlinear multi-agent system is assumed, each agent and the leader has a nonlinear dynamic. It is assumed that at least one agent has access to the state information of the leader, Stability of the error dynamic is equal to consensus of the assumed multi-agent system. Then a fuzzy Lyapunov function is chosen, and some high dimension slack matrix are used, to decouple the Lyapunov´s matrix from the systems´ one and add some degree of freedom to the LMIs. Using some techniques, sufficient conditions for consensus of nonlinear multi-agent systems are converted to LMI constrains. An example for consensus of nonlinear multi-agent systems is solved to show the effectiveness of the main results.