  We consider a two-player zero-sum deterministic differential game where each
player uses both continuous and impulse controls in infinite-time horizon. We
assume that the impulses supposed to be of general term and the costs depend on
the state of the system. We use the dynamic programming principle and viscosity
solutions approach to show existence and uniqueness of a solution for the
Hamilton-Jacobi-Bellman-Isaacs (HJBI) partial differential equations (PDEs) of
the game. We prove under Isaacs condition that the upper and lower value
functions coincide.
