Robust Hurwitz-Schur stability conditions of polytopes of 2-D polynomials

The characteristic polynomials of polytopes of recursive continuous-discrete systems are polytopes of bivariate (2-D) polynomials. Since the root domain of bivariate polynomials is in 2-D complex space, 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 the 1-D case. To solve the problem of the stability test of polytopes of recursive continuous-discrete systems, we establish necessary and sufficient conditions of robust Hurwitz-Schur stability of polytopes of bivariate polynomials. We show that the robust Hurwitz-Schur stability of a polytope of 2-D polynomials can be determined by testing the stability of the edges of the polytope. An example is given to demonstrate the applicability of our approach.