Doyle, John C. and Georgiou, Tryphon T. and Smith, Malcolm C. (1992) The parallel projection operators of a nonlinear feedback system. In: 31st IEEE Conference on Decision and Control. IEEE , Piscataway, NJ, pp. 1050-1054. ISBN 0-7803-0872-7. https://resolver.caltech.edu/CaltechAUTHORS:20190315-103331839
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Abstract
The authors define and study a pair of nonlinear parallel projection operators associated with a nonlinear feedback system. The input-output L_2-stability of a feedback system is shown to be equivalent to a coordinating of the input and output spaces, which is also equivalent to the existence of a pair of nonlinear parallel projection operators onto the graph of the plant and the inverse graph of the controller. These projections have equal norms whenever one of the feedback elements is linear. A bound on this norm is given in the case of passive systems with unity negative feedback.
| Item Type: | Book Section | ||||||||
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| Additional Information: | © 1992 IEEE. Supported in part by the NSF and the AFOSR, U.S.A., and the Nuffield Foundation, U.K. | ||||||||
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| DOI: | 10.1109/CDC.1992.371556 | ||||||||
| Record Number: | CaltechAUTHORS:20190315-103331839 | ||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20190315-103331839 | ||||||||
| Official Citation: | J. C. Doyle, T. T. Georgiou and M. C. Smith, "The parallel projection operators of a nonlinear feedback system," [1992] Proceedings of the 31st IEEE Conference on Decision and Control, Tucson, AZ, USA, 1992, pp. 1050-1054 vol.1. doi: 10.1109/CDC.1992.371556 | ||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||
| ID Code: | 93865 | ||||||||
| Collection: | CaltechAUTHORS | ||||||||
| Deposited By: | Tony Diaz | ||||||||
| Deposited On: | 15 Mar 2019 17:50 | ||||||||
| Last Modified: | 16 Nov 2021 17:01 |
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