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Robust stabilization relative to the unweighted Hnorm is generically unattainable in the presence of singular plant perturbations

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1 Author(s)
Cobb, J.Daniel ; University of Wisconsin-Madison, Madison, WI, USA

Recent work by Vidyasagar gives a sufficient condition under which a singularly perturbed system can be robustly stabilized relative to the unweightedH^{infty}norm. In this note we show that the same condition is also necessary. In addition, we prove that this condition is generically untrue with respect to the class of all linear singularly perturbed systems, as well as the class of all singular perturbations of any fixed, stabilizable, and detectable system.

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Automatic Control, IEEE Transactions on  (Volume:32 ,  Issue: 1 )