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IMA Journal of Mathematical Control and Information 1991 8(4):367-377; doi:10.1093/imamci/8.4.367
© 1991 by Institute of Mathematics and its Applications
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The Unmixing Problem

BENGT MARTENSSON

Institute for Dynamical Systems, University of Bremen P.O. Box 330 440, D-2800 Bremen, Germany bengt{at}mathematik.uni-Bremen.de

High-gain adaptive stabilization of minimum-phase linear systems raises the so-called unmixing problem: finding a finite set A of matrices, with the property that for any M {varepsilon} GL(n), {sigma}(AM) C+ for at least one A . First, some preliminary results will be given, leading up to a non-constructive proof of the existence of such finiteA's. For the cases n = 2 and 3, a fairly satisfying solution is presented. In higher dimensions, the situation is more complicated, and negative results are given. Based on the Euler angles for {delta}O(n), an explicit solution is given for arbitrary n.


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