On the Value of Two-person Zero-sum Linear Quadratic Differential Games

Considered in this paper are the two-person zero-sum linear quadratic differential games. It is shown that the value of the game exists if and only if both the upper value and lower value exist. As an consequence, we prove that another necessary and sufficient condition for the existence of the value of the game is the existence of an open loop-open loop saddle point. An example is also given where lower value exists but upper value does not exist.