Stackelberg strategy in linear quadratic dynamic game for descriptor systems

In this paper the noncooperative linear quadratic game problem will be considered. If the second player is allowed to select his strategy first, he is called the leader of the game and the first player who select his strategy at the second time is called the follower. A stackelberg strategy is the optimal strategy for the leader under the assumption that the follower reacts by playing optimally.We present necessary and sufficient conditions for existence of optimal strategy for linear quadratic continuous non-zero-sum two player dynamic games for index one descriptor system. The connection of the game solution with solution of couple Riccati equation will be studied.