Abstract
This paper investigates the eigenstructure of Hankel operators for non-linear systems. It is proved that the variational system and Hamiltonian extension can be interpreted as the Gâteaux differentiation of dynamical input-output systems and their adjoints respectively. We utilize this differentiation in order to clarify the eigenstructure of the Hankel operator, which is closely related to the Hankel norm of the original system. The results in the paper thus provide new insights to the realization and balancing theory for nonlinear systems.
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Fujimoto, K., Sherpen, J.M.A. (2001). Eigenstructure of nonlinear hankel operators. In: Isidori, A., Lamnabhi-Lagarrigue, F., Respondek, W. (eds) Nonlinear control in the Year 2000. Lecture Notes in Control and Information Sciences, vol 258. Springer, London. https://doi.org/10.1007/BFb0110228
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DOI: https://doi.org/10.1007/BFb0110228
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