Robust Hurwitz stability conditions of polytopes of bivariate polynomials

The necessary and sufficient conditions of robust Hurwitz stability of polytopes of bivariate polynomials have been established. Since the root domain of bivariate polynomials is in C², whose dimension is 4, to be different from that of 1-D polynomials, the analysis for robust stability of polytopes of 2-D polynomials is much more complicated than 1-D case. We develop an edge test for robust Hurwitz stability of 2-D polytopes. An example has been given to demonstrate the applicability of our new approach