Relation between First Order Dynamic Parameters with Pi Control Parameters in Nash Equilibrium

The geometric place of the relation between PI control parameters in Nash equilibrium with respect to dynamic parameters of a first order system was built. The Nash equilibrium was calculated with squared sum of error and squared sum of control signal as players, and the control parameter values as strategies. The geometric place allows the conjecture that exist an homeomorphism. The performance of the regulator in Nash equilibrium is shown.