A Leader-Following Consensus Problem Via a Distributed Observer and Fuzzy Input-to-Output Small-Gain Theorem

This article presents a composite fuzzy distributed control law to solve a cooperative control problem of fuzzy multiagent systems with a nonlinear leader system based on the distributed observer. The contributions of this article are three-fold. First, the small-gain theorem is extended to fuzzy systems, and input-to-output stability (IOS) and output-Lagrange input-to-output stability (OL-IOS) fuzzy small-gain theorem are proposed for fuzzy systems. Second, the OL-IOS small-gain theorem of fuzzy systems with multiple loop is given. Third, based on fuzzy small-gain theorem, the fuzzy distributed control law is composed of a purely fuzzy distributed control law and a distributed observer for the leader system. Finally, the effectiveness of the proposed method is illustrated by using a numerical example and the leader-following consensus problem of the quadrotor.