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.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics