Balanced Realization and Model Order Reduction for Nonlinear Systems based on Singular Value Analysis

This paper discusses balanced realization and model order reduction for both continuous-time and discrete-time general nonlinear systems based on singular value analysis of the corresponding Hankel operators. Singular value analysis clarifies the gain structure of a given nonlinear operator. Here it is proved that singular value analysis of smooth Hankel operators defined on Hilbert spaces can be characterized by simple equations in terms of their states. A balanced realization and model order reduction procedure is derived based on it, and several important properties such as stability, balanced form, Hankel norm, controllability, and observability of the original system are preserved. The work improves the earlier results of [K. Fujimoto and J. M. A. Scherpen, IEEE Trans. Automat. Control, 50 (2005), pp. 2-18] and then continues with new balancing and model reduction results.