Shaping conditions for the robust stability of polynomials with multilinear parameter uncertainty

The author demonstrates that in the case of a polynomial with coefficients which are multilinear in two real parameters, certain shaping conditions guarantee that the -q locus is in general a polygon at each frequency. This facilitates the study of robust stability for a large class of systems and leads to simple conditions for stability of families of polynomials. A physical example is given to demonstrate the approach