An algorithm to form a D-stable coefficient set and its application to the determination of l^2 D-stability radius

This paper concerns the zeros of a polynomial inside a given circle in the left half complex plane. Marden provided an algorithm to determine the number of zeros which a given polynomial has inside the unit circle by using only its coefficents. In this short article, it will be shown that the result can be extended to more general case where the center of the circle is on the real axis and its radius is arbitrary. The execution of the proposed algorithm will produce a set of inequalities which serve as an algebraic expression of a D-stable set in the coefficient space. It should be emphasized that those expressions are suitable for controller design sonsideration in the coefficient space. The determination of l^2 D-stability radius as an application of the result and its related theorem will also be dictated.

Marden's algorithm

coefficient space

zeros of a polynomial

Rouche's theorem

l^2D-stability