  Reach-avoid differential games play an important role in collision avoidance,
motion planning and control of aircrafts, and related applications. The central
problem is the computation of the set of initial states from which the ego
player can enforce the satisfiability of safety specifications over a specified
time horizon. Previous methods addressing this problem mostly focus on finite
time horizons. We study this problem in the context of the infinite time
horizon, where the ego player aims to perpetually force the system to satisfy
certain safety specification while the mutual other player attempts to enforce
a violation of this safety specification. The problem is studied within the
Hamilton-Jacobi reachability framework with unique Lipschitz continuous
viscosity solutions. The continuity and uniqueness property of the viscosity
solution facilitates the use of contemporary numerical methods to solve this
problem with an appropriate number of state variables. An example adopted from
a Moore-Greitzer jet-engine model is employed to illustrate our approach.
