2-D test for robust stability of polytopes of quasipolynomials

The characteristic functions of polytopes of recursive time-delay systems are polytopes of quasipolynomials. Since the roots of quasipolynomials are infinite, to be different from that of 1D polynomials, the analysis for robust stability of polytopes of quasipolynomials is much more complicated than 1D case. By a complex variable transformation in this paper, the quasipolynomials can be regarded 2D hybrid polynomials in s-z domain. Thus, the stability of polytopes of recursive time-delay systems can be determined by the robust Hurwitz-Schur stability of polytopes of 2D polynomials. Furthermore, this paper reveals that the edge stability of a polytope of 2D polynomials is sufficient for the robust stability of polytopes of quasipolynomials, and the edge instability of a polytope of 2D polynomials is necessary for the instability of polytopes of quasipolynomials. An example has been given to demonstrate the applicability of proposed 2D approach