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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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