Simple robust stability tests for polynomials with real parameter uncertainty

Several problems related to the robust stability of polynomials whose coefficients depend on real parameters are considered. it is demonstrated that for certain families where the coefficients themselves are polynomials in the parameters, the determination of stability can be made in a manner that involves a single frequency sweep and where at each frequency a finite number of simple tests are carried out. The methods are based on the Nyquist theorem and value set ideas, and the approach provides analytical solutions