Stability and robustness analysis of minmax solutions for differential graphical games

Recent studies have shown that, in general, Nash equilibrium cannot be achieved by the players of a differential graphical game by using distributed control policies. Alternative solution concepts that do not necessarily lead to Nash equilibrium can be proposed to allow the players in the game determine distributed optimal strategies. This paper analyzes the performance properties of the solution concept regarded as minmax strategies. The minmax formulation is shown to provide distributed control policies for linear systems under mild assumptions. The stability and robustness characteristics of the proposed solution are studied in terms of gain and phase margins, and related to the robustness properties of the single-agent LQR controller. The results of our analysis are finally tested by means of a simulation example.