An L₂ Norm Trajectory-Based Local Linearization for Low Order Systems

This paper presents a linear transformation for low order nonlinear autonomous differential equations. The procedure consists of a trajectory-based local linearization, which approximates the nonlinear system in the neighborhood of its equilibria. The approximation is possible even in the non-hyperbolic case which is of a particular interest. The linear system is derived using an L ₂ norm optimization and the method can be used to approximate the derivative at the equilibrium position. Unlike the classical linearization, the L ₂ norm linearization depends on the initial state and has the same order as the nonlinearity. Simulation results show good agreement of the suggested method with the nonlinear system.