On Certain Topological Invariants Arising in System Theory

Christopher I. Byrnes and Tyrone E. Duncan
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Christopher I. Byrnes: Harvard University, Department of Mathematics and Division of Applied Sciences
Tyrone E. Duncan: University of Kansas, Department of Mathematics

A chapter in New Directions in Applied Mathematics, 1982, pp 29-71 from Springer

Abstract: 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])

Keywords: Homotopy Group; Linear Dynamical System; Topological Invariant; Maslov Index; Hankel Matrix (search for similar items in EconPapers)
Date: 1982
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DOI: 10.1007/978-1-4612-5651-9_3

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