Approximate input-output linearization using L2-optimal bilinearization

In this contribution a numerical method for deriving an approximate input-output linearizing controller for minimum phase systems is presented. The approach is based on the derivation of a bilinear approximation model of higher order, which approximates the considered system on a prespecified multivariable state-space interval. By means of the exact input-output linearizing state feedback of the bilinear model an approximate input-output linearizing controller for the original system with polynomial numerator and denominator is determined. Local stability of the closed-loop system can be assured by subsequently applying a suitable adjustment procedure. The results of the paper are demonstrated by means of a simple example.