The excessive diffusion of multiple unmanned aerial vehicle (UAV) cooperative system may lead to the cooperative failure, but to control the system scale is a potential way to solve this problem. First, macroscopic motion characteristic of multi-UAV cooperative searching system is abstracted, and then motion model of the platform is established. Afterwards, by constructing an appropriate Lyapunov function, the stable control mechanism of this system and its stable control parameters are obtained. Simulation results verify the following two conclusions: 1) the proposed stable control mechanism can not only make multi-UAV system realizes the effective cooperation, but also can ensure the stability of this system; 2) when this system is in a stable state, its scale can be controlled effectively by adjusting the relevant control parameters.