To respond to the Belt and Road initiative, China Southern Power Grid implements grid interconnection with neighboring countries actively, including international synchronous interconnection by AC transmission lines. The safe and stable operation of international interconnected power grid is related to national image and political livelihood. Moreover, the power systen operation information of the connected countries may not be shared fully, which increases difficulty of the international interconnected power grid operation. In this paper, based on the transient angle stability mechanism of multi-machine power system, the effect of completeness of interactive information on transient angle stability is showed. Considering the special case of incomplete interactive information, transient angle instability criterion based on key dynamic characteristic information is studied, then a adaptive switching control strategy for transient angle stability based on completeness of interactive information is proposed. This work provides technical support for the safe and stable operation of international interconnected power grid.