Analysis provides sufficient conditions for robust D-stability in matrix polytopes, suggesting practical applications for stability verification.
In this paper, the robust D-stability of a matrix polytope, defined as the convex hull of a finite set of D-stable matrices, is considered. A sufficient condition for the robust D-stability of the matrix polytope is provided for the region D⊂ C defined as quadratic matrix inequalities (QMI). An algorithm for solving linear matrix inequalities (LMIs) is presented using a convex optimization method based on the maximal eigenvalue function of symmetric matrices. Illustrative examples are provided to demonstrate the applications of this stability condition.
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Şerife Yılmaz (2025) studied this question.
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