\(\mathcal D\)-stability of polynomial matrices. (English) Zbl 1011.93083

Henrion, Didier; Bachelier, Olivier; Šebek, Michael

Int. J. Control 74, No. 8, 845-856 (2001).

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.

Reviewer: Tadeusz Kaczorek (Warszawa)

MSC:

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

Keywords:

linear matrix inequality; complex polynomial matrix; \(D\)-stability; robust stability