Singular value analysis of Hankel operators for general nonlinear systems

This paper discusses singular value analysis of Hankel operators for both continuous-time and discrete-time general nonlinear systems. Singular value analysis clarifies the gain structure of a given operator. Here it is proven that singular value analysis of smooth Hankel operators defined on Hilbert spaces can be characterized by simple equations in terms of their states. A balancing and model reduction procedure is derived based on it. In particular, when the proposed model reduction method is applied to continuous-time nonlinear systems, several gain properties such as Hankel norm, controllability and observability functions are preserved.