ON DELTA-OPERATOR SCHUR-COHN ZERO-LOCATION TESTS FOR FAST SAMPLING

A stability test, or, more generally, a zero location test, algorithm similar to the well-known Schur-Cohn test is proposed when a complex p olynomial formulated in the delta-operator is given. The real polynomi al case falls out naturally as a special case. The method used is a si mple linear transformation based on the Schur-Cohn test, and the propo sed algorithm is computationally efficient. Furthermore, it is shown t hat as the sampling interval vanishes, the new algorithm converges to a new continuous-time test, therefore providing smooth transition from the shift-operator based discrete-time algorithm to the continuous-ti me one. Furthermore, a sensitivity analysis shows that the sensitivity of the new test in the delta operator remains finite with respect to parameter perturbation and converges to that of the continuous-time on e, whereas that of the shift operator grows without bound as the sampl ing interval vanishes. Examples are given to show clear numerical adva ntages over the traditional shift-operator-based Schur-Cohn test in ca se of fast sampling.