摘要
This paper is concerned with the problem of D-stability testing for the interval matrix family. First, a nonlinearly or affine multilinearly parametrized interval polynomial family is considered. If the mapping from the parameter space to the coefficient space can be expressed as an affine linear mapping of at least two variables, then it is shown that the D-stability of the family is equivalent to that of its low dimensional boundaries. In light of this result, it is proved that to determine the D-stability of an interval matrix family,it suffices to check its n!2n(n-1) n-dimensional exposed faces. Finally the results obtained are extended to the case where the rows or the columns of the matrix family are perturbed independently in different polytopes, and a result analogous to that in the interval case is obtained.
This paper is concerned with the problem of D-stability testing for the interval matrix family. First, a nonlinearly or affine multilinearly parametrized interval polynomial family is considered. If the mapping from the parameter space to the coefficient space can be expressed as an affine linear mapping of at least two variables, then it is shown that the D-stability of the family is equivalent to that of its low dimensional boundaries. In light of this result, it is proved that to determine the D-stability of an interval matrix family,it suffices to check its n!2n(n-1) n-dimensional exposed faces. Finally the results obtained are extended to the case where the rows or the columns of the matrix family are perturbed independently in different polytopes, and a result analogous to that in the interval case is obtained.
