Abstract
The boundary preserving properties of a fixed frequency Nyquist mapping from a compact, convex region of uncertainty inR " onto the Horowitz template are investigated via a topological approach. In the casen=2, the boundary preserving properties of the Nyquist mapping and its inverse are shown to be corollaries of the Brouwer domain invariance and the Carathéodory conformal invariance of the boundary. The casen>2 is derived from the casen=2 by taking many two-dimensional slices through the domain. Finally, the edge test results are examined in the light of the Brouwer domain invariance.
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The second author was supported by NSF Grant ECS-95-10656.
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Fathpour, N., Jonckheere, E.A. A Brouwer domain invariance approach to boundary behavior of Nyquist maps for uncertain systems. Math. Control Signal Systems 11, 357–371 (1998). https://doi.org/10.1007/BF02750397
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DOI: https://doi.org/10.1007/BF02750397