With the development of social productivity and the increasing demands of society, mobile manipulators have attracted extensive attention from academia and industry due to their advantages. The industry expects mobile manipulators to accomplish more complex and flexible tasks. However, in many work scenarios, a single mobile manipulator has limited degrees of freedom and payload capacity, leading to the emergence of multi-mobile manipulator systems. This paper establishes the dynamic model of a multi-mobile manipulator system and conducts stability analysis on the dynamic equations. Firstly, the dynamic equation of a single mobile manipulator is established using the Lagrange equations. The correctness of the model is verified by comparing the result obtained from multi-body dynamics software with the numerical calculation result of the dynamics model. Subsequently, the dynamic equations of multiple mobile manipulators and the dynamic equations of the manipulated object are combined to obtain the closed-form dynamic equations of the multi-mobile manipulator system. Then, a Lyapunov function is designed based on joint position error and velocity error, and a control law for joint torques is obtained using the backstepping method. Finally, in the simulation using multi-body dynamics software, the effectiveness of the control law is examined by checking whether the trajectory can track the desired signal.