Abstract
A method to analyze robust stability of parameterized scalar polynomials is generalized to cover parameterized polynomial matrices. A direct solution by calculating the determinant of the parameterized polynomial matrices and then to handling the subsequent scalar problem is not recommended. Appart from possible numerical difficulties, the determinant coefficients are quite complicated functions of those in the given matrix. If the matrix coefficients are not yet fully determined (e.g., if unknown controller parameters are to be fixed as yet by a design procedure), their further “scrambling” makes the analysis more difficult if not impossible. The alternative procedure proposed here is based on a new type of guardian map developed for the matrix case. It completely avoids the need to enumerate the determinant. This feature makes it more suitable if the analysis is to be used in robust control design.
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