Robust stability test for 2-D continuous-discrete systems with interval parameters

摘要

It is revealed that the dynamic stability of 2-D recursive continuous-discrete systems with interval parameters involves the problem of Hurwitz-Schur stability of bivariate polynomials. It is proved that the Hurwitz-Schur stability of the denominator polynomials of the systems is necessary and sufficient for the asymptotic stability of the 2-D hybrid systems. A 2-D hybrid transformation, i.e. 2-D Laplace-Z transform, has been proposed to the stability analysis of the 2-D hybrid transfer functions of the systems. The edge test for the Hurwitz-Schur stability of interval bivariate polynomials is introduced. The Hurwitz-Schur stability of the interval family of 2-D polynomials can be guaranteed by the stability of its finite edge polynomials of the family. An algorithm about the stability test of edge polynomials is given.