Abstract: To guarantee the stability of the overactuated system incorporating the control allocation,a design method is provided to assess optimally the attraction domain of the closed-loop system.The control allocation based overactuated system can be divided into two parts,as inner loop and outer loop.The inner loop realizes the tracking of the pseudo command,while the task of the outer loop is to design the pseudo controller for a square system.The pseudo inverse control allocation is adopted,and under state feedback the attraction domain of the overall system is approached by the ellipsoid through linear matrix inequality(LMI) optimization.The equality between the control allocation based indirect method and the direct method without control allocator is analyzed.The simulation results indicate that the given method can realize zero-error tracking,and guarantee the stability of the closed-loop system.