We study the H-infinity-optimal control problem for semilinear systems in Hilbert spaces in connection with the corresponding H-infinity-problem for the linearized system around an equilibrium state. The result of this paper, which expands some recent results of A. J. van der Schaft, is that if the linearized H-infinity-problem has a suboptimal solution, then a suboptimal solution to the H-infinity-problem for the semilinear system can be constructed in terms of a Hamilton-Jacobi equation.