This paper proposes a method of robust optimal stabilization for balance systems such as rocket and missile systems, Segway human transportation systems, and inverted pendulum systems. Constant-gain controllers such as linear-quadratic regulators may not guarantee stability let alone optimality for balance systems affected by parametric variations. The robust stability and robust performance achieved through the proposed variable-gain controller are better than those of the linear-quadratic regulator. The proposed controller consists of two components, one of which is designed offline for nominal values of parametric variations and one of which is updated online for off-nominal values of parametric variations. A salient feature of the proposed method is a linear transformation that converts the vector control input of balance systems into scalar control input for application of the proposed method. A fourth-order linearized model of an inverted pendulum system is simulated to show the efficacy of the proposed method.