In this paper we consider the following problem: viewing both a nonlinear system model and its linearization as mappings from input-to-state, we define the error between the state of the original nonlinear system and that of the linearization and find the region of the state space where this error is norm-bounded, in the integral-square (or L-2-norm) sense. Using the Hamilton-Jacobi inequality we define the distance between these two systems as the upper bound of this error. (C) 2004 Elsevier Ltd. All rights reserved.