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 polynomial formulated in the delta-operator is given. The real polynomial case falls out naturally as a special case. The method used is a simple linear transformation based on the Schur-Cohn test, and the proposed algorithm is computationally efficient. Furthermore, it is shown that 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-time 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 one, whereas that of the shift operator grows without bound as the sampling interval vanishes. Examples are given to show clear numerical advantages over the traditional shift-operator-based Schur-Cohn test in case of fast sampling.