Robust rank preservation of matrices with both structured and unstructured uncertainties and its applications

Abstract

In this paper, the rank preservation problem is converted to the non-singularity analysis problem of the minors of the matrix under discussion. Under the assumption that a nominal matrix has a specified rank, a sufficient condition is proposed to preserve the assumed property when both structured and 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 preserving the assumed property. The robust controllability problem for linear state-space models with both structured and unstructured parameter uncertainties is given to illustrate the application of the proposed sufficient condition and, for the case when only structured parameter uncertainties are considered, the presented sufficient condition is shown to be less conservative than the existing condition reported in the literature.