Minimax Team Decision Problems

We consider the problem of distributed decision making in a quadratic game between a team of players and nature. Each player has limited information that could be different from the other players in the team. We show that if there is a solution to the minimax team problem, then the linear policies are optimal, and we show how to find the linear optimal solution by solving a linear matrix inequality. The result is used to solve the distributed H
_infin
control problem. It shows that information exchange with neighbours on the graph only, is enough to obtain a linear optimal policy.