## 1 Introduction  
Due to the advantages of high efficiency, high power density, and excellent dynamic response, permanent magnet synchronous motors (PMSMs) are widely applied in industrial production [1, 2, 3]. For modern complex industrial production processes such as electric vehicles, textiles, and aerospace, the speed synchronization control accuracy of multi-motor control systems is a crucial performance indicator determining production quality. Traditional multi-motor speed control systems include master-slave control, cross-coupling control (CCC), deviation coupling control (DCC), and others. In master-slave control, due to the slave motor following the master motor's speed instead of the reference speed, the slave motor's speed always lags behind the master motor, resulting in significant synchronization errors during startup and when the slave motors experience load disturbances, leading to chattering in the slave motors [4]. Therefore, the concept of CCC strategy is proposed, using the speed difference between two motors as the feedback signal to achieve speed control of multiple motors. Reference [5] designed a CCC system based on model predictive, effectively solving chattering in the speed regulation system. However, when the CCC method is extended to more than two motors, it significantly impacts the synchronous performance of the motors. To address this issue, DCC was proposed based on CCC. Reference [6] proposed a mean DCC strategy for multi-motor speed regulation systems, which can improve the synchronization performance of the system. Traditional coupling control strategies provide an effective method for achieving speed coordination control in multi-motor systems. However, the introduction of the coupling structure causes mutual influence between tracking control and synchronization control, making it difficult to balance both performances. Additionally, it lacks flexibility, as changes in the number of motors require modifications to the original coupling structure. To achieve synchronized control, the rotational speed information of all motors in the system must be obtained, which leads to a complex structure. As the scale of the multi-motor system increases, traditional coordinated control methods struggle to meet real-time computational requirements [7]. Nowadays, multi-agent systems (MASs) are widely applied because of the advantages of flexibility, reliability, and strong self-organizing capabilities. MASs composed of simple agents are often used to address distributed control problems, such as aerial vehicle formations [8], multi-robot systems [9], and rail transit [10]. Considering the fundamental similarity between the consensus control in MASs and the speed cooperative control in multi-motor systems, each motor system can be regarded as an agent, and graph theory can be employed to depict communication among agents. Introducing the concept of consensus into multi-motor speed cooperative control systems and leveraging the superior synchronization capability of multi-agents to achieve speed synchronization control for multi-motor speed cooperative control systems. This provides a novel approach and means for addressing the speed collaborative control problem in multi-motor speed cooperative control systems. Based on the convergence time of MASs, it can be categorized into various types, such as the asymptotic consensus, the finite-time consensus, and the fixed-time consensus. Reference [11] introduces an asymptotic exponential consensus to ensure convergence in handling MASs with uncertain agent dynamics. Compared to the asymptotic exponential consensus, the finite-time consensus offers advantages such as faster convergence speed and better robustness to external uncertainties [12]. The finite-time convergence implies that a MAS reaches the desired consensus or synchronization state within a finite amount of time.