Linear-quadratic zero-sum differential games for generalized state space systems

In this note, we consider linear-quadratic zero-sum differential games for generalized state space systems. It is well known that a unique linear feedback saddle-point solution can exist in the game of state space systems. However, for the generalized state space system, we show that the game admits uncountably many linear feedback saddle-point solutions. Sufficient conditions for the existence of Linear feedback saddlepoint solutions are found. A constructive method is given to find these linear feedback saddle-point solutions. A simple example is included to illustrate the nonuniqueness of the linear feedback saddle-point solutions