A Computational Geometry Approach to Simplicial Nyquist Maps in Robust Stability (1994)
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author = {Edmond Jonckheere Murilo and Murilo G. Coutinho and Chih-yung Cheng},
title = {A Computational Geometry Approach to Simplicial Nyquist Maps in Robust Stability},
booktitle = {In Proc. American Control Conf},
year = {1994},
pages = {1901--5}
}
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Abstract:
In this paper we use combinatorial and computational geometry techniques to make the simplicial approximation theorem a computational, rather than conceptual, tool to check robust stability for systems that are not in Kharitonov's class. A simplicial program was developed with a O(n log n) time complexity, where n is the cardinality of the vertex set of points mapped to the complex plane, using the Nyquist map f . Keywords: Topology, computational geometry, simplicial approximation. 1. Introduction Robustness of stability is a crucial issue in robust control. In multivariable control theory, it is well known that the stable multivariable loop transmission L(jw) remains stable after closing the loop if and only if det(I + L(jw)) 6= 0; 8w 2 R, provided that the plot of det(I + L(jw)) does not encircle the origin 0 + j0. In order to check stability for all pertubations 4 2 D, where D is a topological space of structured uncertainties, we define the Nyquist map: f : D \Theta\Omega !...
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