Consensus of T-S Fuzzy Fractional-Order, Singular Perturbation, Multi-Agent Systems

Due to system complexity, research on fuzzy fractional-order, singular perturbation, multi-agent systems (FOSPMASs) remains limited in control theory. This article focuses on the leader-following consensus of fuzzy FOSPMASs with orders in the range of 0, 2. By employing the T-S fuzzy modeling approach, a fuzzy FOSPMAS is constructed. In order to achieve the consensus of a FOSPMAS with multiple time-scale characteristics, a fuzzy observer-based controller is designed, and the error system corresponding to each agent is derived. Through a series of equivalent transformations, the error system is decomposed into fuzzy singular fractional-order systems (SFOSs). The consensus conditions of the fuzzy FOSPMASs are obtained based on linear matrix inequalities (LMIs) without an equality constraint. The theorems provide a way to tackle the uncertainty and nonlinearity in FOSPMASs with orders in the range of 0, 2. Finally, the effectiveness of the theorems is verified through an RLC circuit model and a numerical example.