In this paper, we present a transformation approach for solving the Hamilton-Jacobi-Bellman equations (HJBEs) arising in H-2 or quadratic-cost control of nonlinear deterministic and stochastic systems. We show that the HJBE can be solved analogously to a scalar quadratic equation, and we give a parameterization of solutions to the HJBE characterizing the solution of the optimal control problem. The procedure is also generalized to include nonsmooth or viscosity solutions of the (S)HJBE. (C) 2003 Elsevier Science Ltd. All rights reserved.