Abstract
This paper is an extension of the lecture presented by the first author at the conference, New Directions in Applied Mathematics, held at The Cleveland Museum of Art and at The Case Western Reserve University on the occasion of that university’s centennial anniversary. This author would like to thank the organizers of the conference, Professors Peter Hilton and Gail Young, for their cordial invitation to join in CWRU’s celebration as well as for the opportunity to give such a lecture at a time when the mathematics of control systems is expanding quite rapidly on several exciting frontiers. The lecture itself covered, roughly speaking, the material treated in sections 1, 3, and 5 of the present paper and was intended to give an indication of the kind of research which is currently going on in the application of geometry and topology to the problems and theory of linear systems. These topics included a survey of known results and of joint work with the second author, and with R. W. Brockett (this has been reported in more detail elsewhere [10])
Research partially supported by the National Aeronautics and Space Administration under Grant NSG-2276, the National Science Foundation under Grant NEG-79-09459, and the Air Force Office of Scientific Research under Grant AFOFR-81-0054.
Research partially supported by the U.S. Air Force Office of Scientific Research Grant 77-3177, by the U.S. Office of Naval Research under the Joint Services Electronics Program Contract N00014-75-0648 at Harvard, and as a guest of the SFB 72 of the Deutsche Forschungsgemeinschaft, Bonn.
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Byrnes, C.I., Duncan, T.E. (1982). On Certain Topological Invariants Arising in System Theory. In: Hilton, P.J., Young, G.S. (eds) New Directions in Applied Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5651-9_3
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