Abstract
In this paper we extend the elimination lemma to hold for a set of inequalities. The elimination lemma is a linear algebra result which has been successfully used to solve a large number of filtering and control problems. We show that the obtained extension can be used to provide alternative solutions to robust state feedback control and robust filtering problems when the uncertainty is described by a convex polytope. We also investigate some conjectures which, if true, would be able to solve an open problem in dynamic output feedback robust control. We provide counter-examples to these conjectures.
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