Hankel Operators and Gramians for Nonlinear Systems

W. Steven Gray, Jacquelien M.A. Scherpen

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16 Citaten (Scopus)
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In the theory for continuous-time linear systems, the system Hankel operator plays an important role in a number of realization problems ranging from providing an abstract notion of state to yielding tests for state space minimality and algorithms for model reduction. But in the case of continuous-time nonlinear systems, Hankel theory is considerably less developed beyond a well known Hankel mapping introduced by Fliess in 1974. In this paper, a definition of a system Hankel operator is developed for causal L2-stable input-output systems. If a generating series representation of the input-output system is given then an explicit representation of the corresponding Hankel operator is possible. If, in addition, an affine state space model is available with certain stability properties then a unique factorization of the Hankel operator can be constructed with direct connections to well known and new nonlinear Gramian extensions.
Originele taal-2English
TitelProceedings of the 37th IEEE Conference on Decision and Control, 1998
UitgeverijUniversity of Groningen, Research Institute of Technology and Management
Aantal pagina's6
ISBN van geprinte versie0780343948
StatusPublished - 1998
Evenement37th IEEE Conference on Decision and Control, Tampa, Florida, USA -
Duur: 16-dec-199818-dec-1998


Conference37th IEEE Conference on Decision and Control, Tampa, Florida, USA

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