The dynamic programming equation (DPE) corresponding to nonlinear H-infinit
y control is considered. When the cost grows quadratically in the state,,it
is well known that there may be an infinite number of viscosity solutions
to the DPE. In fact, there may be more than one classical solution when a c
lassical solution exists. For the case of fixed feedback control, it is sho
wn that there exists a unique viscosity solution in the class of solutions
meeting a certain growth condition, and a representation in terms of availa
ble storage is obtained. For the active control case, where the H-infinity
problem is represented by a differential game, a similar representation res
ult is obtained under the assumption of existence of a suboptimal feedback
control.