Robust \(D\)-stability via positivity (Q1304049)

The authors approach the problem of robust \(D\)-stability of a complex polynomial by converting it to positivity in the real domain of the magnitude function. In this way the stability test can be performed by means of the Bernstein subdivision algorithm which requires only real arithmetic. The criterion for Hurwitz stability is applied to the stability study of polynomials with interval parameters and polynomial uncertainty structures. A significant result refers to the stopping criterion in connection with the situation of a large number of iterations, a case which corresponds to at least one zero closer than a prescribed limit to the imaginary axis.