On robust stability of polynomials with polynomial parameter dependency - Two/three parameter cases

Real polynomials whose coefficients depend polynomially on the elements of an uncertain parameter vector are considered. The smallest destabilizing perturbation defines the stability radius of the set of uncertain polynomials. It is shown that determining this radius is equivalent to solving a finite set of systems of algebraic equations and picking out the real solution with the smallest norm. The number of systems of equations depends crucially on the dimension of the parameter vector, whereas the complexity of systems of equations increases mainly with the kind of polynomial dependency and the degree of the polynomial. (C.A.B.)