Abstract: Hybrid differential game combines the control engineering, mathematics and computer science. The research has a high value no matter in theory or in practical applications. In this paper, the discriminating domain of hybrid differential game with two targets and two players is discussed based on this theory. Firstly, the discriminating domain of continuous differential game on a region where the functions are piecewise smooth is discussed using nonsmooth analysis. Then, we find that the problem of determining the discriminating domain can be transformed into determining the solution of the inequalities. Finally, the result is generalized to the hybrid differential game. The novelty is that we propose the method of discriminating domain for differential game which contains two control variables, not one control variable as in differential inclusion.

Key words: hybrid differential game, discriminating domain, piecewise smooth function