This paper addresses the leader-follower non-fragile consensus of nonlinear fractional-order (FO) multi-agent systems (FOMAS) with state time delay. The structured uncertainties occurring in both the plant and the controller are considered for the first time. Using the linear matrix inequality approach and the FO Razumikhin theorem, a delay- and order-dependent protocol is obtained to guarantee the leader-follower non-fragile consensus of the FOMAS with uncertain parameters. New sufficient conditions for the leader-follower non-fragile consensus of FO linear multi-agent systems are presented. The feasibility and effectiveness of the protocol proposed is verified with three numerical examples. Compared with the existing schemes, the approach reveals good robustness and can be extended to different kinds of consensus problems.

本文讨论了具有状态时间延迟的非线性分数阶 (FO) 多智能体系统 (FOMAS) 的领导者-跟随者非脆弱共识。首次考虑了工厂和控制器中出现的结构化不确定性。使用线性矩阵不等式方法和 FO Razumikhin 定理，获得了延迟和顺序相关的协议，以保证具有不确定参数的 FOMAS 的领导者 - 跟随者非脆弱共识。提出了 FO 线性多智能体系统的领导者 - 追随者非脆弱共识的新充分条件。通过三个数值例子验证了所提出协议的可行性和有效性。与现有方案相比，该方法具有良好的鲁棒性，可以扩展到不同类型的共识问题。