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\(\mathcal D\)-stability of polynomial matrices. (English) Zbl 1011.93083
An interesting general LMI methodology is proposed for determining whether the zeros of a given complex polynomial matrix \(A(s)\) belong to a given region of the complex plane. Necessary and sufficient conditions for \(D\)-stability of the polynomial matrix are established. The method does not require the computation of the matrix determinant or its zeros. The \(D\)-stability conditions can be combined with other LMI conditions arising in robust stability analysis.

MSC:
93D09 Robust stability
15A39 Linear inequalities of matrices
90C22 Semidefinite programming
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