Singular Value Analysis Of Nonlinear Symmetric Systems

Ionescu, T. C., Fujimoto, K. & Scherpen, J. M. A., Sep-2011, In : IEEE Transactions on Automatic Control. 56, 9, p. 2073-2086 14 p.

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In this paper, we introduce the notions of state-space symmetry for nonlinear systems and of the cross operator as a non-trivial natural extension of the linear symmetric case, in terms of the controllability and observability operators associated to it. We give a characterization of a symmetric nonlinear system in terms of the cross operator and a coordinate transformation. Then we analyze the use of the cross operator for solving the Hankel singular value problem of the system. The result is a new and simpler characterization of the solutions of this problem in terms of the cross operator and a metric.

Original languageEnglish
Pages (from-to)2073-2086
Number of pages14
JournalIEEE Transactions on Automatic Control
Issue number9
Publication statusPublished - Sep-2011


  • Balancing, cross operator, Hankel, nonlinear systems, singular value, symmetry, DYNAMICAL-SYSTEMS, MODEL IDENTIFICATION, HAMILTONIAN-SYSTEMS, REDUCTION, REPRESENTATIONS

ID: 5399278