Robust rank preservation of matrices with both structured and unstructureduncertainties and its applications

In this paper. the rank preservation problem is converted to the non-singul arity analysis problem of the minors of the matrix under discussion. Under the assumption that a nominal matrix has a specified rank, a sufficient con dition is proposed to preserve the assumed property when both structured an d unstructured parameter uncertainties are added to the nominal matrix. The proposed sufficient condition can provide the explicit relationship of the bounds on both structured and unstructured parameter uncertainties for pre serving the assumed property. The robust controllability problem for linear state-space models with both structured and unstructured parameter uncerta inties is given to illustrate the application of the proposed sufficient co ndition and. for the case when only structured parameter uncertainties are considered, the presented sufficient condition is shown to be less conserva tive than the existing condition reported in the literature.