Guaranteed Cost Strategy for Hierarchical Game in Financial Systems: LMIs-Constrained Method

This paper deals with the hierarchical game for a financial market system. Firstly, the differential game is utilized to balance the control performance and disturbance. Managers and investors pursue their own interests which are partly conflicting with others. Subsequently, the noncooperative game is applied to multiperson noncooperative decision making problem of financial market. Based on the optimal solution of the differential game, the guaranteed cost strategy is designed by a linear matrix inequality (LMI)-constrained method. Finally, a numerical example is provided to verify the validity and advantages of the proposed methodology.