Aimed at the issues of structural complexity and high computational burden for permanent magnet synchronous motor (PMSM) traditional coupled control methods, a novel finite-time leader-following speed cooperative control method based on a multi-agent system is proposed. Relying on an undirected communication topology, a distributed finite-time speed consensus protocol is constructed based on the multi-agent mathematical model of PMSMs. Meanwhile, in order to deal with uncertain disturbances and unmodeled dynamics in the system, a super-twisting extended state observer (STESO) is introduced for real-time estimation, and the observation results are incorporated into the consensus protocol for compensation, thereby deriving the desired q-axis current. Furthermore, by constructing a Lyapunov function, rigorous theoretical proof of the finite-time convergence of the proposed controller is provided, along with an upper bound estimate of the convergence time. Finally, comparative experiments with the deviation coupling control algorithm are carried out on an experimental platform comprising three PMSM speed regulation systems. Results show that under conditions of speed variation, load changes, and forward-reverse rotation, the proposed method exhibits superior performance the maximum speed jitter is reduced from 3 r/min with the traditional method to below 0.5 r/min, synchronization error is significantly decreased, and the speed can recover smoothly and rapidly to the set value under load disturbances. Experimental results verify that the proposed scheme achieves high synchronization accuracy, fast convergence, and strong robustness, and provides an effective solution for high-performance multi-motor cooperative control.