Hankel Operators and Gramians for Nonlinear Systems

W. Steven Gray, Jacquelien M.A. Scherpen

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

16 Citations (Scopus)
431 Downloads (Pure)


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.
Original languageEnglish
Title of host publicationProceedings of the 37th IEEE Conference on Decision and Control, 1998
PublisherUniversity of Groningen, Research Institute of Technology and Management
Number of pages6
ISBN (Print)0780343948
Publication statusPublished - 1998
Event37th IEEE Conference on Decision and Control, Tampa, Florida, USA -
Duration: 16-Dec-199818-Dec-1998


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

Cite this