1996 Volume 9 Issue 9 Pages 426-434
In this paper, a computational method of the formal linearization by a cubic Hermite interpolation is proposed. A discrete nonlinear system represented by nonlinear difference equation is converted into an approximated linear system. We introduce a linearizing function that consists of the state variables, their squares, and the cubes. The nonlinear terms are approximated in the form of piecewise cubic polynomials by the cubic Hermite interpolation and linearized with respect to the linearizing function. Numerical computations are very easy because both the conversion into the linear system and the inversion are done by simple matrix calculations. Error analysis of the linearization is discussed. As an application of the linearization a nonlinear filter is synthesized. Through some numerical examples, the accuracy of the linearization and the state estimation is improved as the size of subdomain is shortened.
