LP-Based Leader-Following Positive Consensus of T-S Fuzzy Multi-Agent Systems

This paper investigates the leader–follower consensus problem for T-S fuzzy multi-agent systems with positive constraints by designing observer-based control protocols, where the T-S fuzzy model is mainly used to characterize the nonlinearity in the system. First, a stable system is chosen as the leader. Then, a fuzzy observer that satisfies the positivity condition is constructed for follower agents. Meanwhile, an observer-based fuzzy controller design is proposed using a matrix decomposition approach. On this basis, the positivity and asymptotic consensus of the system are achieved by a set of sufficient conditions in the form of linear programming. Subsequently, an unstable system is chosen as the leader. A virtual target is introduced. By means of the co-positive Lyapunov function and linear programming approach, an observer and controller are designed to ensure both positivity and practical consensus of systems. Compared to existing literature, the consideration of positivity constraints and the linear programming-based observation-control scheme expand the application scope of multi-agent systems while reducing the computational burden. Finally, two illustrative examples are provided to verify the effectiveness of the obtained results.