Bounds on generalized structured singular values via the Perron root of matrix majorants

Abstract The purpose of this paper is to present several bounds upon the structured singular value. We first adopt a generalized notion of the structured singular value which is useful for problems where uncertainties are assumed to be bounded in an l p - induced matrix norm. Two different type of bounds, in terms of Perron root and interaction parameters respectively, are given for the new structured singular value and their relations are discussed. These bounds are useful in that they are easy to compute and may be further analyzed to provide insights useful in design.

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