We introduce a performance-guaranteed limbic system-inspired control (LISIC) strategy for nonlinear multi-agent systems (MASs) with uncertain high-order dynamics and external perturbations, where each agent in the MAS incorporates a LISIC structure to support the consensus controller. This novel approach, which we call double integrator LISIC (DILISIC), is designed to imitate double integrator dynamics after closing the agent-specific control loop, allowing the control designer to apply consensus techniques specifically formulated for double integrator agents. The objective of each DILISIC structure is then to identify and compensate model differences between the theoretical assumptions considered when tuning the consensus protocol and the actual conditions encountered in the real-time system to be controlled. A Lyapunov analysis is provided to demonstrate the stability of the closed-loop MAS enhanced with the DILISIC. Additionally, the stabilization of a complex system via DILISIC is addressed in a synthetic scenario: the consensus control of a team of flexible single-link arms. The dynamics of these agents are of fourth order, contain uncertainties, and are subject to external perturbations. The numerical results validate the applicability of the proposed method.