Successive linearizations of second order multidimensional time-invariant systems

The present paper discusses a linearization method for second order multidimensional time-invariant systems. The method approximates locally the nonlinear vector field around the equilibrium, where the solution starting from a given initial state near the equilibrium is approximated by a linear solution. This linearization is usually called local trajectory-based linearization. The approximation is computed using an iterative method, which consists of successive approximations in the least square sense. Using a numerical example, it is shown that the linearized solutions exhibit good agreement with the nonlinear solutions.  2004 Elsevier B.V. All rights reserved. PACS: 02.60.-x; 02.60.Cb; 02.60.Lj