A Formal Linearization for a General Class of Time-varying Nonlinear Systems by the Cubic Hermite Interpolation and a Nonlinear Observer

A computational method of the formal linearization for time-varying nonlinear systems by using the cubic Hermite interpolation is proposed. We introduce a linearizing function that consists of the state variables, their squares, and the cubes. The nonlinear terms are approximated by the cubic Hermite interpolation and thus a formal linear time-varying system with respect to the linearizing function is acquired. The execution of this method is easily carried out by simple matrix multiplications. A nonlinear observer is synthesized as an application of this method and is verified through numerical example