Speeding up an Algorithm for Checking Robust Stability of Polynomials

The paper considers the robust stability veriication of polynomials with polynomial parameter dependency. A new algorithm is presented which relies on the expansion of a multivariate polynomial into Bernstein polynomials and is based on the inspection of the value set of the family of polynomials on the imaginary axis. It is shown how an initial interval on the imaginary axis through which zero crossing of members of the family is only possible is Obtained by applying known bounds for the positive zeros of a polynomial. This interval can be improved by using again Bernstein expansion, thereby speeding up the algorithm considerably.