Perturbations, Singular Values, and Ranks of Partial Triangular Matrices
Leiba Rodman, Hugo J. Woerdeman · SIAM Journal on Matrix Analysis and Applications · 1995
Questions regarding minimal representations of perturbations of discrete systems lead to the study of perturbations of lower triangular partial matrices and their minimal rank completions. Distance to the set of lower triangular partial matrices having minimal ranks smaller than a given integer is given in terms of (suitably generalized) singular numbers. Minimal ranks of lower triangular partial matrices in an arbitrary small neighborhood of a given lower triangular partial matrix are identified. The results are applied to minimal representations of discrete systems.