Immittance 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 a scattering-type tabular test based on Jury's modified stability test. Here an immittance-type counterpart for the test, that relies instead on a modified form of the author's test, is presented. The immittance 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 a bivariate polynomial of degree (n, n)).