A numerical approach to approximate input-output linearization of nonlinear systems

This paper presents an approximate input-ouput linearization approach for nonlinear nonminimum phase systems. A special Byrnes-Isidori normal form is introduced where the internal dynamics are approximately decoupled into its stable and antistable part. Furthermore, the antistable part of the internal dynamics is approximately linear. By using this nonlinear input-ouput normal form an approximately input-output linearizing controller achieving an internally stable closed loop system can be easily derived. The corresponding change of coordinates is computed by solving a linear matrix equation which is derived in explicit form. Consequently, the proposed approach can be readily implemented in a numerical software package. A simple example demonstrates the results of the paper.