H∞ Consensus of Nonlinear Multi-agent Systems on Undirected Topology Based on Polynomial Fuzzy Model

For nonlinear leader-follower multi-agent systems with undirected topology, this paper presents a new H_∞ consensus design approach via polynomial fuzzy model. Firstly, the polynomial fuzzy model are constructed to described the error dynamics between the follower agents and the leader. Then, the polynomial fuzzy controller is designed that guarantees the error states converging to zero in short time. Polynomial Lyapunov functional is utilized for stability analysis of the error system. Moreover, the proposed fuzzy model is extended to solve the synchronization problem of nonlinear systems. H_∞ control protocol is designed to synchronize the response system and the drive one, and preserve an H_∞ performance index. All the design conditions can be represented as sum of squares problem, and are numerical solved. Finally, illustrative example is given to demonstrate the effectiveness of obtained theoretical results.