Relaxed Consensus Condition for IT-2 Fuzzy Model Multi-Agent Systems With Dynamic Communication Topologies in a Leader-Following Framework

This article investigates the leader-following consensus problem of second-order multi-agent systems (MASs) with uncertain dynamics and dynamic communication topologies by employing an interval type-2 (IT-2) fuzzy model to capture imprecisions in both the system dynamics and the network structures. To more realistically represent time-varying interconnections, fuzzy-rule-dependent Laplacian and leader adjacency matrices are formulated, directly linking the communication structures to fuzzy rules. Building on this modeling framework, a distributed adaptive control scheme is developed under a non-parallel distributed compensation (non-PDC) structure. Furthermore, a crisp aggregated-function-dependent Lyapunov function is supported, thereby enhancing flexibility in controller synthesis. In particular, by identifying and exploiting five fundamental relationships between fuzzy basis functions (FBFs) and their crisp counterparts, the proposed approach establishes a systematic relaxation technique that transforms the controller design into less conservative linear matrix inequalities (LMIs) conditions. The effectiveness and practicality of the proposed method are validated through simulations of robotic manipulators, in which the followers successfully achieve asymptotic tracking of the leader's position and velocity despite nonlinearities and dynamically varying communication topologies.