Spectral Unmixing of Classes of Arbitrary Nonsingular Matrices

Abstract It has been shown that for any nonsingular matrix M, there exists a finite set of ‘unmixing’ matrices S such that at least one member Si ϵ S will exhibit the property that MSi will be stable, i.e. MSi will be a Hurwitz Matrix. The purpose of this note is to construct such a set for the cases n = 2, 3 and for the specific case of companion matrices of arbitrary dimension. A direct application of such ‘unmixing’ matrices is in the construction of adaptive-type controllers using switching controllers.

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