Abstract:  This paper investigates  the saddle-point equilibrium of quadratic differential game for singular bilinear systems in the finite time. As it is complex to solve the problem, a reduced-order transformation is introduced in order to obtain the fast and slow subsystems, then, the optimal control is obtained by using the maximum principle. In the end, the simulation of a numerical example is presented to illustrate the correctness and effectiveness of the proposed algorithm.

Key words: singular bilinear system, differential game, saddle-point equilibrium