TheL-dominance concept and its applications to multivariable system designs
Lam Fat Yeung, G.F. Bryant · International Journal of Control · 1992
A new type of dominance measure based on triangular factorizations is developed and is named the L-dominance measure. This new measure is tighter than any existing dominance measures and in particular is tighter than those based on generalized dominance and M-matrix theory. The L-dominance condition on matrices with non-positive off-diagonal elements is proved to be equivalent to the M-matrix condition. But in contrast to the M-matrix condition, the testing of the L-dominance condition is easier and can be carried out in sequential order. Furthermore, these special properties enable us to construct a synthesis based design procedure superior to those based on generalized dominance or M-matrix theory; the last two methods are generally regarded as post-mortem analytical tools only.