Efficient stability tests: unifying theory and further results using the delta operator

The delta operator has shown great promise in unifying efficient stability tests of given system characteristic polynomials. In this paper some of these results are first briefly reviewed which then set the stage for presenting further results in this subject. Specifically, we present efficient tests in the singular case and results of a sensitivity analysis. The limits of such tests in the singular case are shown to be those of the continuous-time ones. The sensitivity analysis not only proves the improved numerical property of the delta-operator based tests over the traditional shift-operator based ones, it also shows that the sensitivities of the delta operator based tests converge to those of the continuous-time ones as the sampling period approaches zero.