Immitance and telepolation-based procedures to test stability of continuous-discrete bivariate polynomials

The paper presents several algebraic procedures to test whether a bivariate polynomial is continuous-discrete (C-D) stable (does not vanish in the product of the closed right-half-plane times the closed exterior of the unit circle). This problem was solved in the last ISCAS by scattering-type tabular test has a lower cost of computation because it produces a sequence of matrices with para-conjugate column symmetry. Telepolation-based forms for the two tabular tests are also presented. They carry out the C-D stability test by a finite number of Jury´s or this author´s 1-D stability tests, respectively, plus a Routh zero location procedure. As a consequence the overall complexity reduces significantly (from O(n⁶) to O(n⁴) for bivariate polynomial of degree (n, n)).