On the stability of uncertain polynomials with dependent coefficients

A sufficient condition is given for reducing the conservatism of the stability bounds for a family of polynomials with dependent coefficients, including nonlinear coefficients. It is also proved that if a finite family of stable polynomials has the same even part, then the polynomial with the even part and the odd part formed by adding any positive multiple of the even parts and odd parts, respectively, of the given family is also stable. Similar results holds if the given family of polynomials has the same odd part. A numerical example with nonlinear coefficients is given to illustrate the technique, and it is observed that the stability bounds obtained are larger than those acquired by Kharitonov´s theorem