In this article we study balanced model reduction of linear control systems using the singular perturbation approximation. Balanced model reduction techniques have been successfully applied to systems with homogeneous initial conditions, with one of their most important features being a priori L 2 and H ∞ bounds for the approximation error. The main focus of this work is to derive an L 2 error bound for the singular perturbation approximation for system with inhomogeneous initial conditions, extending related work on balanced truncation. This L 2 error bound measures the difference between the input-output maps of the original and of the reduced initial value systems. The advantages and flexibility of this approach are demonstrated with a variety of numerical examples. © 2019 Elsevier Inc.