Computing the distance between a nonlinear model and its linear approximation: an L2 approach

In this paper we consider the following problem: viewing both a nonlinear system model and its linearization as mappings from input-tostate, 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 L2-norm) sense. Using the Hamilton–Jacobi inequality we define the distance between these two systems as the upper bound of this error. ©