$H_{\infty }$ Consensus and Synchronization of Nonlinear Systems Based on A Novel Fuzzy Model

This paper investigates the H_∞ consensus control problem of nonlinear multiagent systems under an arbitrary topological structure. A novel Takagi-Sukeno (T-S) fuzzy modeling method is proposed to describe the problem of nonlinear follower agents approaching a time-varying leader, i.e., the error dynamics between the follower agents and the leader, whose dynamics is evolving according to an isolated unforced nonlinear agent model, is described as a set of T-S fuzzy models. Based on the model, a leader-following consensus algorithm is designed so that, under an arbitrary network topology, all the follower agents reach consensus with the leader subject to external disturbances, preserving a guaranteed H_∞ performance level. In addition, we obtain a sufficient condition for choosing the pinned nodes to make the entire multiagent network reach consensus. Moreover, the fuzzy modeling method is extended to solve the synchronization problem of nonlinear systems, and a fuzzy H_∞ controller is designed so that two nonlinear systems reach synchronization with a prescribed H_∞ performance level. The controller design procedure is greatly simplified by utilization of the proposed fuzzy modeling method. Finally, numerical simulations on chaotic systems and arbitrary nonlinear functions are provided to illustrate the effectiveness of the obtained theoretical results.