Abstract
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Hankel operator are studied and yield promising results.
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Ionescu, T.C., Scherpen, J.M.A. (2009). Nonlinear Cross Gramians. In: Korytowski, A., Malanowski, K., Mitkowski, W., Szymkat, M. (eds) System Modeling and Optimization. CSMO 2007. IFIP Advances in Information and Communication Technology, vol 312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04802-9_16
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DOI: https://doi.org/10.1007/978-3-642-04802-9_16
Publisher Name: Springer, Berlin, Heidelberg
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