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Sponsored by the Center for Science and Technology Development of the Ministry of Education
Supervised by Ministry of Education of the People's Republic of China
The characteristic polynomials of polytopes of recursive 2-D 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 1-D case. To solve the problem of 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 has been given to demonstrate the applicability of our new approach.
Keywords:polytopes of bivariate polynomials, robust Hurwitz-Schur stability, test theorems