State-space formulas are derived for a family of controllers solving the nonlinear H-infinity-output feedback control problem, The formulas given are expressed in terms of the solutions to two Hamilton-Jacobi inequalities in n independent variables. These controllers are obtained by interconnecting the "central controller" with an asymptotically stable, free system having L(2)-gain less than or equal to gamma. All proofs given are simple and clear and provide deeper insight in the synthesis of the corresponding linear H-infinity controllers.