This note is devoted to the problem of robust stability of interval parameter matrices. Based on some basic facts relating the H∞ norm of a transfer function to the Riccati matrixinequality and Hamilton matrix, sever...This note is devoted to the problem of robust stability of interval parameter matrices. Based on some basic facts relating the H∞ norm of a transfer function to the Riccati matrixinequality and Hamilton matrix, several test conditions with parameter perturbation bounds are obtained.展开更多
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 t...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.展开更多
文摘This note is devoted to the problem of robust stability of interval parameter matrices. Based on some basic facts relating the H∞ norm of a transfer function to the Riccati matrixinequality and Hamilton matrix, several test conditions with parameter perturbation bounds are obtained.
文摘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.
