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On mappable nonlinearities in robustness analysis
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DOI：10.1109/9.506246.png)
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Abstract
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When carrying out robustness analysis in the frequency domain, the following fundamental problem arises: Given a description of the uncertain quantities entering the system, at each frequency omega, we need to carry out a mapping into the complex plane. For the special case of multilinear uncertainty structures, the Mapping Theorem greatly facilitates this process and leads to the convex hull of the value set of interest. In this paper, we generalize the class of nonlinear uncertainty structures for which the convex hull can be generated-the so-called Generalized Mapping Theorem goes considerably beyond the multilinear setting. For example, this new framework leads to mappability for large classes of polynomic and nonlinear uncertainty structures, The formulas associated with convex hull generation are seen to be easily implemented in two-dimensional graphics.
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