Model reduction for nonlinear systems based on the differential eigenstructure of Hankel operators

This paper offers a new input-normal output-diagonal realization and model reduction procedure for nonlinear systems based on the differential eigenstructure of Hankel operators. Firstly, we refer to the preliminary results on input-normal realizations with original singular value functions and the differential eigenstructure of Hankel operators with axis singular value functions. Secondly, the relationship between the two different characterizations of singular value functions is clarified and, consequently, the new input-normal realization is characterized. Thirdly, we perform the model reduction based on the obtained realization. Furthermore numerical examples demonstrate the effectiveness of the proposed method.